Question

complete the parts below. write your answers as whole numbers or fractions in simplest form. (a) a pizza parlor makes batches of pizza dough. they use a ratio of 3 grams of garlic powder to 15 grams of salt. give two different unit rates using this relationship. one unit rate: select for each select another unit rate: select for each select (b) how many grams of garlic powder are needed if 10 grams of salt are used? grams of garlic powder

Explanation:

Part (a)

We have a ratio of garlic powder to salt as \(3:15\) (simplify this ratio first).

Step 1: Simplify the ratio

The ratio of garlic powder to salt is \(3\) grams : \(15\) grams. Simplify this by dividing both by \(3\), we get \(1\) gram : \(5\) grams. So one unit rate is \(1\) gram of garlic powder for each \(5\) grams of salt.

Step 2: Find another unit rate

We can also express the ratio as salt to garlic powder. From the original ratio \(3:15\), if we consider salt per garlic powder, divide both by \(3\), we get \(5\) grams of salt for each \(1\) gram of garlic powder. So another unit rate is \(5\) grams of salt for each \(1\) gram of garlic powder.

Part (b)

We know the ratio of garlic powder to salt is \(3:15\) or simplified \(1:5\) (garlic powder : salt). Let \(x\) be the grams of garlic powder when salt is \(10\) grams.

Step 1: Set up the proportion

Using the ratio \(\frac{\text{garlic powder}}{\text{salt}}=\frac{3}{15}=\frac{x}{10}\)

Step 2: Solve for \(x\)

Simplify \(\frac{3}{15}=\frac{1}{5}\), so \(\frac{1}{5}=\frac{x}{10}\). Cross - multiply: \(5x = 10\times1\), then \(x=\frac{10}{5}=2\)

Answer:

s:
(a) One unit rate: \(1\) gram of garlic powder for each \(5\) grams of salt; Another unit rate: \(5\) grams of salt for each \(1\) gram of garlic powder.

(b) \(\boldsymbol{2}\) grams of garlic powder are needed.