Math  /  Algebra

QuestionTrey sold t-shirts and hats at a festival. His total profit was 93.Hemadea93. He made a 3 profit for each t-shirt he sold. He also made a profit of $45 from selling hats. How many t-shirts did he sell? (a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 93, 3, and 45. Let x represent the number of t-shirts. x + +0 = 0 0-0-0 ° 0 0 X G (b) Solve the equation in part (a) to find the number of t-shirts. x = 0

Studdy Solution

STEP 1

What is this asking? How many t-shirts did Trey sell if he made a total profit of $93\$93, with $3\$3 profit per t-shirt and $45\$45 profit from hats? Watch out! Don't forget that the $45\$45 hat profit is separate from the t-shirt profit!

STEP 2

1. Set up the equation
2. Solve for x

STEP 3

Alright, let's break this down!
We know Trey's **total profit** was $93\$93.
This total profit comes from two sources: selling t-shirts and selling hats.

STEP 4

He makes $3\$3 for each t-shirt.
If xx is the number of t-shirts he sold, his profit from t-shirts is 3x3 \cdot x.

STEP 5

His profit from hats is $45\$45.

STEP 6

So, the **total profit** ($93\$93) is the sum of the t-shirt profit (3x3 \cdot x) and the hat profit ($45\$45).
This gives us the equation: 3x+45=933 \cdot x + 45 = 93

STEP 7

Our goal is to get xx all by itself!
First, we want to isolate the term with xx, so let's subtract $45\$45 from **both sides** of the equation.
Remember, what we do to one side, we *must* do to the other to keep the equation balanced! 3x+4545=93453 \cdot x + 45 - 45 = 93 - 45 3x+0=483 \cdot x + 0 = 483x=483 \cdot x = 48

STEP 8

Now, we have 3x=483 \cdot x = 48.
To get xx by itself, we need to divide **both sides** by 33.
Think of it as dividing to one, since 3/3=13/3=1. 3x3=483\frac{3 \cdot x}{3} = \frac{48}{3} 1x=161 \cdot x = 16x=16x = 16

STEP 9

Trey sold **16** t-shirts.

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