Question

7.2.02

1. a bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. complete the table so that it shows a proportional relationship between the amount of honey and the amount of flour. show or explain your thinking.

spiral review
problems 8 - 10: solve each equation. show your thinking.

1. $\frac{1}{2}+x = 2$
2. $\frac{2}{3}y = 6$
3. $3=\frac{1}{4}b$
4. a student makes a scaled copy of a rectangle. the dimensions of the original rectangle are 3.5 - by - 2.5 meters. select all the possible dimensions of the scaled copy.

a. 1.75 meters and 1.25 meters
b. 7 meters and 5 meters
c. 7 meters and 6 meters
d. 10 meters and 2.5 meters
e. 10.5 meters and 7.5 meters
reflection

1. put a question mark next to a problem you were feeling stuck on.
2. use this space to ask a question or share something youre proud of.

Explanation:

Problem 7

Step1: Find the ratio of honey to flour

The ratio of honey to flour is $\frac{8}{10}=\frac{4}{5}$.

Step2: Find flour when honey is 20

Let the amount of flour be $x$. Since the ratio is $\frac{4}{5}$, we have $\frac{20}{x}=\frac{4}{5}$, cross - multiply gives $4x = 20\times5$, so $x=\frac{20\times5}{4}=25$.

Step3: Find flour when honey is 13

Let the amount of flour be $y$. Then $\frac{13}{y}=\frac{4}{5}$, cross - multiply gives $4y=13\times5$, so $y = \frac{13\times5}{4}=16.25$.

Step4: Find honey when flour is 12.5

Let the amount of honey be $z$. Then $\frac{z}{12.5}=\frac{4}{5}$, cross - multiply gives $5z=12.5\times4$, so $z=\frac{12.5\times4}{5}=10$.

Step1: Isolate the variable $x$

Subtract $\frac{1}{2}$ from both sides of the equation $\frac{1}{2}+x = 2$. So $x=2-\frac{1}{2}$.

Step2: Calculate the value of $x$

$x=\frac{4 - 1}{2}=\frac{3}{2}=1.5$.

Step1: Solve for $y$

Multiply both sides of the equation $\frac{2}{3}y = 6$ by $\frac{3}{2}$ to isolate $y$. So $y=6\times\frac{3}{2}$.

Step2: Calculate the value of $y$

$y = 9$.

Answer:

Honey (tbsp)	Flour (cups)
20	25
13	16.25
10	12.5

Problem 8