Q52. - Algebra 1

Question

At The Family Farm, you can pick your own fruits and vegetables.

The Family Farm
Apples	$6.99/bag$
Pumpkins	$5.00each$
Blueberries	$2.99/qt$
Winter squash	$2.99each$

1. The cost of a bag of potatoes is \(1.50 less than $\frac{1}{2}$ of the price of apples. Write and solve an equation to find the cost of potatoes.
2. The price of each zucchini is 3 times the price of winter squash minus \)7. Write and solve an equation to find the cost of zucchini.
3. Write an equation to represent the cost of pumpkin using the cost of blueberries.

Step-by-Step Solution

Answer

1. The cost of potatoes bag is $\$1.995$.
2. The cost of zucchini is $\$1.97$.
3. The equation that represents the cost of pumpkin using the cost of blueberries is $p=2b-0.98$.

a. Step 1. Determine the variable.

Let the cost of a bag of potatoes is represented by x.

Step 2. Determine the equation.

It is given that the cost of a bag of potatoes is $\$1.50$ less than $\frac{1}{2}$ of the price of apples. The cost of apples is $6.99/bag$.

Thus, the required equation is: $x=\frac{1}{2}\left(6.99\right)-1.50$

Step 3. Simplify.

$\begin{array}{l}x=\frac{1}{2}\left(6.99\right)-1.50\\ x=3.495-1.50\\ x=1.995\end{array}$

Hence, the cost of a bag of potatoes is $\$1.995$.

b. Step 1. Determine the variable.

Let the price of each zucchini is represented by z.

Step 2. Determine the equation.

It is given that the price of each zucchini is 3 times the price of winter squash minus $7.

The cost of winter squash is $2.99each$.

Thus, the required equation is: $z=3\left(2.99\right)-7$

Step 3. Simplify.

$\begin{array}{l}z=3\left(2.99\right)-7\\ z=1.97\end{array}$

Hence, the cost of zucchini is $\$1.97$.

c. Step 1. Determine the variable.

Let the cost of a pumpkin is represented by p.

Let the cost of blueberries is represented by b.

Step 2. Determine the equation.

$\begin{array}{l}Thecostofis2timesthecostofminus0.98\\ apumpkinblueberries\\ p=2\times b-0.98\end{array}$

Step 3. Write the equation.

$p=2b-0.98$

Hence, the equation that represents the cost of pumpkin using the cost of the blueberries is $p=2b-0.98$.