I just emailed you requesting a change of date for this week's math club meeting. Please let me know if you could move the date from Wednesday 10/13 to Thursday or Friday morning.
1. The ratio of girls to boys in Mrs. Franks’ 7th-grade class is 3/4 (excluding Mrs. Franks). On Monday, 4 girls and 6 boys got to go on a special field trip for honor roll students. Since no other students were absent on Monday, the ratio of girls remaining in the class to boys remaining in the class was 4/5. How many students are in Mrs. Franks’ class when everyone is present?
2. On the field trip Abbey, Bethany, Christine and Darcy bought a total of 4 hot dogs and 3 sodas, which cost the girls $17.00 before tax. Edward (one of the boys on the field trip) bought 2 hot dogs and 1 soda from the same lunch stand and it cost him $7.80 before tax. How much would 1 hot dog and 1 soda cost at the lunch stand before tax?
3. On the same day, 32 students from the 8th grade got to go on a field trip to the zoo. When they returned to the school after the field trip the students were asked to answer a couple of survey questions. One of the questions asked “Which animal did you like best, the elephants or the lions?”. When all of the surveys had been turned in, 20 students had selected elephants and 22 had selected lions. If all of the students selected at least one of the two choices, how many students selected both lions and elephants?
1. The ratio of girls to boys is normally 3/4, which is the same as 3x/4x. After 4 girls leave and 6 boys leave we can represent the number of girls and the number of boys as 3x – 4 and 4x – 6, respectively. We are told that the ratio becomes 4/5 when the field trip students leave, thus we can set up the equation (3x – 4)/(4x – 6) = 4/5. Now we crossmultiply and solve for x. 5(3x – 4) = 4(4x – 6) --> 15x – 20 = 16x – 24 --> 4 = x That means there are normally 3(4) = 12 girls in the class and 4(4) = 16 boys in the class, giving us a total of 12 + 16 = 28 students.
2. To solve this one we should first set up two equations using the two totals that were provided in the question. (Let h = cost of a hotdog and s = cost of a soda) 4h + 3s = 17.00 2h + 1s = 7.80 By subtracting the second equation from the first we find that 2h + 2s = 9.20. Thus, the cost of 1 hotdog and 1 soda is 9.20/2 = $4.60.
3. Since all of the students selected at least one of the choices and there were 20 + 22 = 42 “best” animal choices made, 42 – 32 = 10 students must have selected both animals.
In an effort to restore the number of native hardwood trees growing in the Chesapeake Watershed region, the Potomac Conservancy has started the “Growing Native” project. Each fall they hold nut collections, at which Nut Buddies can drop off the nuts (acorns, walnuts, etc) they have collected from their local area. The nuts, which are actually the seeds of the tree, are then planted and grown until the spring when the saplings are planted along rivers and streams. The trees are important because they help clean the water that they live next to.
1. A class at St. Joe’s Day School collected acorns, “helicopter” seeds and walnuts in the ratio of 3:2:7, respectively. What is the least number of seeds the class could have collected?
2. Five years ago on October 12, Mr. Venner’s class planted an oak tree that grows at a rate of 1.5 feet per year. Last year on October 12, Mr. Venner’s class planted a walnut tree that grows at a rate of 2 feet per year. After how many more years will the walnut tree be the same height as the oak tree?
3. Next spring Martha plans to plant trees along the edge of a stream. The area in which she will be planting is 76 ft long. If she plans to give each tree a 1 ft by 1 ft square plot and to leave 4 feet of space between each plot, what is the maximum number of trees she could fit in the 76 ft long stretch of land?
2. The oak tree is 5(1.5) = 7.5 feet tall. The walnut tree is 1(2) = 2 feet tall. If we let the number of years that pass from now be represented by y, we can make the equation: 7.5 + 1.5y = 2 + 2y. Thus, by solving for y we find that it will take 0.5y = 5.5 --> y = 11 more years for the two trees to be equal height.
3. Grouping 1 plot with 1 space we see that we are dealing with 1 ft + 4 ft = 5 ft sections of land, however, 5 doesn’t go into 76 evenly, so we know there is some extra space after the 15th 5-foot section. Through multiplication, we see that the 15 5-foot sections take up 75 feet of space, which leaves 76 ft – 75 ft = 1 ft left at the end. That 1 foot is exactly enough space for 1 more tree. Thus, the greatest number of trees that would fit in the 76 foot stretch of shore is 15 + 1 = 16 trees.
Hi Mr. P!
ReplyDeleteI just emailed you requesting a change of date for this week's math club meeting. Please let me know if you could move the date from Wednesday 10/13 to Thursday or Friday morning.
Thanks,
Agni
P.S. I'm glad we have a Math Club blog! :)
Problems:
ReplyDelete1. The ratio of girls to boys in Mrs. Franks’ 7th-grade class is 3/4 (excluding Mrs. Franks).
On Monday, 4 girls and 6 boys got to go on a special field trip for honor roll students.
Since no other students were absent on Monday, the ratio of girls remaining in the class
to boys remaining in the class was 4/5. How many students are in Mrs. Franks’ class
when everyone is present?
2. On the field trip Abbey, Bethany, Christine and Darcy bought a total of 4 hot dogs and 3
sodas, which cost the girls $17.00 before tax. Edward (one of the boys on the field trip)
bought 2 hot dogs and 1 soda from the same lunch stand and it cost him $7.80 before tax.
How much would 1 hot dog and 1 soda cost at the lunch stand before tax?
3. On the same day, 32 students from the 8th grade got to go on a field trip to the zoo. When
they returned to the school after the field trip the students were asked to answer a couple
of survey questions. One of the questions asked “Which animal did you like best, the
elephants or the lions?”. When all of the surveys had been turned in, 20 students had
selected elephants and 22 had selected lions. If all of the students selected at least one of
the two choices, how many students selected both lions and elephants?
Hey Agni,
ReplyDeleteI tried #3 and the answer I got was 10. Is that correct?
Thanks,
Nidhi G.
Yes! The answer to number 3 is 10.
ReplyDeleteTry the other 2. I'll send the solutions later.
Mr. Pearson said he would be putting a pass on here! I don't have one for tomorrow!
ReplyDeleteSolutions to the above problems:
ReplyDelete1. The ratio of girls to boys is normally 3/4, which is the same as 3x/4x. After 4 girls leave
and 6 boys leave we can represent the number of girls and the number of boys as 3x – 4
and 4x – 6, respectively. We are told that the ratio becomes 4/5 when the field trip
students leave, thus we can set up the equation (3x – 4)/(4x – 6) = 4/5. Now we crossmultiply
and solve for x.
5(3x – 4) = 4(4x – 6) --> 15x – 20 = 16x – 24 --> 4 = x
That means there are normally 3(4) = 12 girls in the class and 4(4) = 16 boys in the class,
giving us a total of 12 + 16 = 28 students.
2. To solve this one we should first set up two equations using the two totals that were
provided in the question. (Let h = cost of a hotdog and s = cost of a soda)
4h + 3s = 17.00
2h + 1s = 7.80
By subtracting the second equation from the first we find that 2h + 2s = 9.20. Thus, the
cost of 1 hotdog and 1 soda is 9.20/2 = $4.60.
3. Since all of the students selected at least one of the choices and there were 20 + 22 = 42
“best” animal choices made, 42 – 32 = 10 students must have selected both animals.
Problems Set 2
ReplyDeleteIn an effort to restore the number of native hardwood trees growing in the Chesapeake Watershed region, the Potomac Conservancy has started the “Growing Native” project. Each fall they hold nut collections, at which Nut Buddies can drop off the nuts (acorns, walnuts, etc) they have collected from their local area. The nuts, which are actually the seeds of the tree, are then planted and grown until the spring when the saplings are planted along rivers and streams. The trees are important because they help clean the water that they live next to.
1. A class at St. Joe’s Day School collected acorns, “helicopter” seeds and walnuts in the ratio of 3:2:7, respectively. What is the least number of seeds the class could have collected?
2. Five years ago on October 12, Mr. Venner’s class planted an oak tree that grows at a rate of 1.5 feet per year. Last year on October 12, Mr. Venner’s class planted a walnut tree that grows at a rate of 2 feet per year. After how many more years will the walnut tree be the same height as the oak tree?
3. Next spring Martha plans to plant trees along the edge of a stream. The area in which she will be planting is 76 ft long. If she plans to give each tree a 1 ft by 1 ft square plot and to leave 4 feet of space between each plot, what is the maximum number of trees she could fit in the 76 ft long stretch of land?
Where do you get all these problems? Is the club next week on Monday?
ReplyDeleteDear Mr. Pearson,
ReplyDeleteI'll not be able to attend the Math Club meeting this Monday 10/25, for I have an orchestra rehearsal.
Agni
Solutions - Problems Set 2
ReplyDelete1. 3 + 2 + 7 = 12
2. The oak tree is 5(1.5) = 7.5 feet tall. The walnut tree is 1(2) = 2 feet tall. If we let the number of years that pass from now be represented by y, we can make the equation: 7.5 + 1.5y = 2 + 2y. Thus, by solving for y we find that it will take 0.5y = 5.5 --> y = 11 more years for the two trees to be equal height.
3. Grouping 1 plot with 1 space we see that we are dealing with 1 ft + 4 ft = 5 ft sections of land, however, 5 doesn’t go into 76 evenly, so we know there is some extra space after the 15th 5-foot section. Through multiplication, we see that the 15 5-foot sections take up 75 feet of space, which leaves 76 ft – 75 ft = 1 ft left at the end. That 1 foot is exactly enough space for 1 more tree. Thus, the greatest number of trees that would fit in the 76 foot stretch of shore is 15 + 1 = 16 trees.
This comment has been removed by the author.
ReplyDeleteMathmagichian Agni, will you please translate the problem set one explanations to make a 6th grader understand them? Thank you!
ReplyDelete