Question

1. a grocery store receives a 180-pound crate containing six 10-pound bags of potatoes and an unknown number of 5-pound bags of potatoes.

a. write an equation to find the number of 5-pound bags of potatoes in the crate.
b. how many 5-pound bags of potatoes are in the crate?

1. natalia paid $38.95 for three medium-sized pizzas and a salad. if natalia paid $11.98 for the salad, how much did each pizza cost?

Explanation:

Problem 4a

Step1: Define variable

Let \( x \) be the number of 5 - pound bags.

Step2: Calculate weight from 10 - pound bags

The weight of six 10 - pound bags is \( 6\times10 = 60\) pounds.

Step3: Calculate weight from 5 - pound bags

The weight of \( x \) 5 - pound bags is \( 5x \) pounds.

Step4: Write the equation

The total weight of the crate is 180 pounds, so the equation is \( 60 + 5x=180 \).

Step1: Start with the equation from 4a

We have the equation \( 60+5x = 180 \).

Step2: Subtract 60 from both sides

\( 60 + 5x-60=180 - 60 \), which simplifies to \( 5x=120 \).

Step3: Divide both sides by 5

\( \frac{5x}{5}=\frac{120}{5} \), so \( x = 24 \).

Step1: Define variable

Let \( p \) be the cost of each pizza.

Step2: Calculate total cost of pizzas

The total cost of three pizzas is \( 3p \) dollars.

Step3: Write the equation

The total amount paid is the cost of pizzas plus the cost of the salad. So \( 3p+11.98 = 38.95 \).

Step4: Subtract 11.98 from both sides

\( 3p+11.98 - 11.98=38.95 - 11.98 \), which simplifies to \( 3p = 26.97 \).

Step5: Divide both sides by 3

\( \frac{3p}{3}=\frac{26.97}{3} \), so \( p = 8.99 \).

Answer:

\( 60 + 5x = 180 \)

Problem 4b