SAT Ratios and Proportions Practice

It's given that Anita used a ratio of 2 ounces of blue paint to 3 ounces of yellow paint for the first batch. For any batch of paint that uses the same ratio, the amount of yellow paint used will be $\frac{3}{2}$, or 1.5, times the amount of blue paint used in the batch.

Therefore, the amount of yellow paint Anita will use in the second batch will be 1.5 times the amount of blue paint used in the second batch. Alternate approach: It's given that Anita used a ratio of 2 ounces of blue paint to 3 ounces of yellow paint for the first batch and that she will use 5 ounces of blue paint for the second batch.

A proportion can be set up to solve for $x$, the amount of yellow paint she will use for the second batch: $\frac{2}{3}=\frac{5}{x}$. Multiplying both sides of this equation by 3 yields $\frac{2}{x}=\frac{15}{x}$, and multiplying both sides of this equation by $x$ yields $2x=15$.

Dividing both sides of this equation by 2 yields $x=7.5$. Since Anita will use 7.5 ounces of yellow paint for the second batch, this is $\frac{7.5}{5}=1.5$ times the amount of blue paint (5 ounces) used in the second batch.

The correct answer is $980$. It's given that the ratio $140$ to $m$ is equivalent to the ratio $4$ to $28$.

Therefore, the value of $m$ can be found by solving the equation $\frac{140}{m}=\frac{4}{28}$. Multiplying each side of this equation by $m$ yields $140=\frac{4m}{28}$.

Multiplying each side of this equation by $28$ yields $3920=4m$. Dividing each side of this equation by $4$ yields $980=m$.

Therefore, the value of $m$ is $980$.

It's given that Shaquan has 7 red cards and 28 blue cards.

Therefore, the ratio of red cards to blue cards that Shaquan has is 7 to 28.

This ratio can be reduced by dividing both parts of the ratio by 7, which yields the ratio 1 to 4.