3 cups of the 11% flour and 3 cups of the 63% flourD. 9 cups of the 11% flour and 9 cups of the 63% flour19. A science teacher has a supply of 5% hydrochloric acid and a supply of 65% hydrochloric acid (HCl). How much of each solution should the teacher mix together to get 42 mL of 45% HCl for an experiment?A. The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.......
18. A baker has a bag of flour that is 11% whole wheat and a bag of flour that is 63% whole wheat. How many cups of each type does the baker need to make 12 cups of a flour mixture that is 50% whole wheat?
A. 3 cups of the 11% flour and 9 cups of the 63% flour
B. 9 cups of the 11% flour and 3 cups of the 63% flour
C. 3 cups of the 11% flour and 3 cups of the 63% flour
D. 9 cups of the 11% flour and 9 cups of the 63% flour
19. A science teacher has a supply of 5% hydrochloric acid and a supply of 65% hydrochloric acid (HCl). How much of each solution should the teacher mix together to get 42 mL of 45% HCl for an experiment?
A. The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.
B. The teacher will need 28 mL of the 5% solution and 14 mL of the 65% solution.
C. The teacher will need 14 mL of the 5% solution and 14 mL of the 65% solution.
D. The teacher will need 28 mL of the 5% solution and 28 mL of the 65% solution.
MY ANSWERS
3. A
4. C
5. D
6. B
10. B
11. C
14. A
15. D
16. C
17. A
18. B
19. D
Your answers to 10 and 15 are correct. The remainder are not.
3-6
When one equation is a multiple of the other, as in x+4y=4, 2x+8y=8, then they both describe the same line. There will be an infinite number of solutions, as every point on the line satisfies both equations.
When the equations have the same coefficients, but different constants, they describe parallel lines. There will be zero solutions, as no point will be on both lines. Example: y-6x=2, y-6x=4.
10-15
Check your answer. Try the selected answer in all of the given equations to verify it works.
16-17
You have costs and you have (more or less) offsets to those costs. When those are balanced, you have some incremental revenue from each sale and some amount of residual cost it must cover. Dividing the residual cost by the increment per sale will tell you how many sales you need to make. (A $5 ticket pays for a $3 bat and gives $2 in incremental revenue.)
18-19
There's a cute way to work mixture problems. Write down the high contributor over the low contributor, and the target between. Then "cross subtract" putting the difference from the target to the low contributor next to the high contributor and vice versa.
63% ... 39% (difference from low contributor)
... \ ...... /
.......50% (target)
... / ...... \
11% ... 13% (difference from high contributor)
This tells you the ratio of parts of high-contributor to low-contributor is 39:13, or 3:1. If you want a total of 12 parts, that will be 9:3 parts of 63% flour to 11% flour.
Note, too, that the closer the target is to the high value, the larger the proportion of high-contributor you have. This can help you check your answer.
