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Question Linda sold tt-shirts at a festival, earning $65\$ 65 after paying $10\$ 10 for her booth. She earned $5\$ 5 per tt-shirt. Write an equation to find the number of tt-shirts she sold.

Studdy Solution

STEP 1

Assumptions
1. Linda went home with 65aftersellingt−shirts.<br/>2.Shepaid65 after selling t-shirts.<br />2. She paid 10 for her booth.
3. She earned 5foreacht−shirtsold.<br/>4.Weneedtofindthenumberoft−shirtssold,representedbythevariable5 for each t-shirt sold.<br />4. We need to find the number of t-shirts sold, represented by the variable x$.

STEP 2

First, we need to write an equation that represents the situation. The total amount Linda went home with is the amount she earned from selling t-shirts minus the cost of the booth.
Total earned=(Amount earned per t−shirt×Number of t−shirts)−Booth costTotal\, earned = (Amount\, earned\, per\, t-shirt \times Number\, of\, t-shirts) - Booth\, cost

STEP 3

Let's represent the number of t-shirts sold by xx. The amount earned per t-shirt is 5andtheboothcostis5 and the booth cost is 10. We can now write the equation using these variables.
65=5x−1065 = 5x - 10

STEP 4

We have the equation in the form:
5x−10=655x - 10 = 65
This corresponds to the second form in the problem statement:
□x−□=□\square x - \square = \square

STEP 5

Now we fill in the blanks with the correct numbers:
5x−10=655x - 10 = 65

STEP 6

For part (b), we need to write an expression that represents the amount Linda earned from selling t-shirts. This expression does not include the booth cost.
Amount earned from t−shirts=Amount earned per t−shirt×Number of t−shirtsAmount\, earned\, from\, t-shirts = Amount\, earned\, per\, t-shirt \times Number\, of\, t-shirts

STEP 7

Using the variable xx to represent the number of t-shirts sold, and knowing she earned $5 per t-shirt, the expression is:
5x5x

STEP 8

Now we solve the equation from STEP_5 to find the number of t-shirts sold. First, we add 10tobothsidestoisolatethetermwith10 to both sides to isolate the term with x$.
5x−10+10=65+105x - 10 + 10 = 65 + 10

STEP 9

Simplify both sides of the equation.
5x=755x = 75

STEP 10

Now, divide both sides by 5tosolvefor5 to solve for x$.
5x5=755\frac{5x}{5} = \frac{75}{5}

STEP 11

Calculate the value of xx.
x=15x = 15
Linda sold 15 t-shirts.

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