Question

1. maddie scored 7 kills in 3 games. at that rate, how many games will it take her to score 20 kills?
2. the ratio of pizzelles to biscotti were 4 to 3. if there were 72 pizzelles, how many biscotti were there?

Explanation:

Question 11

Step1: Define the rate

The rate of kills per game is $\frac{7}{3}$ kills per game.

Step2: Set up the proportion

Let $x$ be the number of games to score 20 kills. We have the proportion $\frac{7}{3}=\frac{20}{x}$.

Step3: Solve for $x$

Cross - multiply: $7x = 3\times20$. So, $7x=60$. Then $x=\frac{60}{7}\approx8.57$. Since we can't have a fraction of a game in a practical sense, and if we consider the rate, we can also think of it as: first find how many games per kill, which is $\frac{3}{7}$ games per kill. Then for 20 kills, the number of games is $20\times\frac{3}{7}=\frac{60}{7}\approx9$ (if we round up because she can't play a fraction of a game and needs to reach 20 kills). But mathematically, the exact value is $\frac{60}{7}\approx8.57$.

Step1: Define the ratio

The ratio of pizzelles to biscotti is $4:3$. Let the number of pizzelles be $4y$ and the number of biscotti be $3y$.

Step2: Find the value of $y$

We know that $4y = 72$. Solve for $y$: $y=\frac{72}{4}=18$.

Step3: Find the number of biscotti

The number of biscotti is $3y$. Substitute $y = 18$ into it: $3\times18 = 54$.

Answer:

$\frac{60}{7}\approx8.6$ (or 9 if we round up to the nearest whole number of games)

Question 13