Solved on Feb 02, 2024

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

STEP 1

Assumptions
1. Linda went home with $65 after selling t-shirts.<br />2. She paid$ 10 for her booth.
3. She earned $5 for each t-shirt sold.<br />4. We need to find the number of t-shirts sold, represented by the variable$ 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.
$Total\, earned = (Amount\, earned\, per\, t-shirt \times Number\, of\, t-shirts) - Booth\, cost$

STEP 3

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

STEP 4

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

STEP 5

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

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.
$Amount\, earned\, from\, t-shirts = Amount\, earned\, per\, t-shirt \times Number\, of\, t-shirts$

STEP 7

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

STEP 8

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

STEP 9

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

STEP 10

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

STEP 11

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

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

STEP 1

Assumptions
1. Linda went home with $65 after selling t-shirts.<br />2. She paid$ 10 for her booth.
3. She earned $5 for each t-shirt sold.<br />4. We need to find the number of t-shirts sold, represented by the variable$ 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.
$Total\, earned = (Amount\, earned\, per\, t-shirt \times Number\, of\, t-shirts) - Booth\, cost$

STEP 3

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

STEP 4

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

STEP 5

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

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.
$Amount\, earned\, from\, t-shirts = Amount\, earned\, per\, t-shirt \times Number\, of\, t-shirts$

STEP 7

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

STEP 8

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

STEP 9

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

STEP 10

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

STEP 11

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

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

STEP 1

STEP 2

STEP 3

Let's represent the number of t-shirts sold by xxx. The amount earned per t-shirt is 5andtheboothcostis5 and the booth cost is 5andtheboothcostis10. We can now write the equation using these variables.65=5x−1065 = 5x - 1065=5x−10

STEP 4

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

STEP 5

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

STEP 6

STEP 7

Using the variable xxx to represent the number of t-shirts sold, and knowing she earned $5 per t-shirt, the expression is:5x5x5x

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 10tobothsidestoisolatethetermwithx$.5x−10+10=65+105x - 10 + 10 = 65 + 105x−10+10=65+10

STEP 9

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

STEP 10

Now, divide both sides by 5tosolvefor5 to solve for 5tosolveforx$.5x5=755\frac{5x}{5} = \frac{75}{5}55x​=575​

STEP 11

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

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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

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

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

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

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

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

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

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

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