Question

4.
to make a shade of paint called jasper green, mix 4 quarts of green paint with $\frac{2}{3}$ cup of black paint. how much green paint should be mixed with $4\frac{1}{2}$ cups of black paint to make jasper green?

5.
a grocer can buy strawberries for $1.38 per pound.
a. write an equation relating $c$, the cost, and $p$, the pounds of strawberries.

6.
match each situation with a diagram.

a
diagram a: two bars, top bar labeled $x$ with 4 shaded and 3 unshaded sections, bottom bar labeled $y$ fully shaded

b
diagram b: two bars, top bar labeled $x$ with 4 shaded sections, bottom bar labeled $y$ with 4 shaded sections (shorter than $x$)

c
diagram c: two bars, top bar labeled $x$ with 4 shaded sections, bottom bar labeled $y$ with 1 shaded section (much shorter than $x$)

1. diego drank $x$ ounces of juice. lin drank $\frac{1}{4}$ less than that.
2. lin ran $x$ miles. diego ran $\frac{3}{4}$ more than that.
3. diego bought $x$ pounds of almonds. lin bought $\frac{1}{4}$ of that.

Explanation:

Problem 4

Step1: Set up proportion

Let $g$ = green paint (quarts). Proportion: $\frac{4}{\frac{2}{3}} = \frac{g}{4\frac{1}{2}}$

Step2: Convert mixed number to fraction

$4\frac{1}{2} = \frac{9}{2}$

Step3: Solve for $g$

$g = 4 \times \frac{3}{2} \times \frac{9}{2}$
$g = 6 \times \frac{9}{2}$
$g = 27$

Step1: Relate cost to pounds

Cost = price per pound × pounds

• Diagram A: $x$ is split into 7 parts, $y$ equals all 7 parts. This matches situation 2: Lin ran $x$ (4 parts), Diego ran $\frac{3}{4}$ more, so $y = x + \frac{3}{4}x = \frac{7}{4}x$ (7 parts).
• Diagram B: $x$ is 4 parts, $y$ is 3 parts. This matches situation 1: Diego drank $x$ (4 parts), Lin drank $\frac{1}{4}$ less, so $y = x - \frac{1}{4}x = \frac{3}{4}x$ (3 parts).
• Diagram C: $x$ is 4 parts, $y$ is 1 part. This matches situation 3: Diego bought $x$ (4 parts), Lin bought $\frac{1}{4}$ of that, so $y = \frac{1}{4}x$ (1 part).

Answer:

27 quarts

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Problem 5a