Question

more working with proportion
sometimes, the information given in a proportion question requires you to take a
different approach to solving. this occurs when two parts are mixed to make something
new, and the parts are then compared to the new mixture rather than each other.
example: susan is making lemonade. to make her lemonade, she mixes four parts of
water with one part of lemon juice. if she wants to make 15 cups of lemonade,
how many cups of water and how many cups of lemon juice does she need?
solution: since the ratio is 4:1, this means there are 5 parts in total in the lemonade.
when solving this problem, one proportion is needed for each part of the
ratio, comparing that part with the final mixture.
water:
\\(\frac{\text{water}}{\text{lemonade}}\\) \\(\frac{4}{5} = \frac{x}{15}\\)
so \\(x = 4 \times 15 \div 5 = 12\\) cups of water
lemon juice: \\(\frac{\text{lemon juice}}{\text{lemonade}}\\) \\(\frac{1}{5} = \frac{x}{15}\\)
so \\(x = 1 \times 15 \div 5 = 3\\) cups of lemon juice
assignment 5 – more working with proportion

1. the ratio of flour to butter in a recipe for pie crust is 2:1. if a baker makes 30 cups of

piecrust, how many cups of flour and how many cups of butter does he need?

1. two chemicals are mixed where the ratio of chemical a to chemical b is 3:12. if

there are 45 l of the mixture, how much of each chemical is in the mixture?

Explanation:

(Problem 1):

Step1: Find total parts

Total parts = $2 + 1 = 3$

Step2: Solve for flour amount

Set up proportion: $\frac{\text{flour}}{\text{piecrust}} = \frac{2}{3} = \frac{x}{30}$
$x = \frac{2 \times 30}{3} = 20$

Step3: Solve for butter amount

Set up proportion: $\frac{\text{butter}}{\text{piecrust}} = \frac{1}{3} = \frac{y}{30}$
$y = \frac{1 \times 30}{3} = 10$

(Problem 2):

Step1: Find total parts

Total parts = $3 + 12 = 15$

Step2: Solve for Chemical A amount

Set up proportion: $\frac{\text{Chemical A}}{\text{mixture}} = \frac{3}{15} = \frac{m}{45}$
$m = \frac{3 \times 45}{15} = 9$

Step3: Solve for Chemical B amount

Set up proportion: $\frac{\text{Chemical B}}{\text{mixture}} = \frac{12}{15} = \frac{n}{45}$
$n = \frac{12 \times 45}{15} = 36$

Answer:

1. Flour: 20 cups, Butter: 10 cups
2. Chemical A: 9 L, Chemical B: 36 L