A local charity sold T-shirts and coffee mugs to raise funds, earning a total of \18t + 12m = 2,316tm70$ coffee mugs, how many T-shirts did it sell?

Solution available with step-by-step explanation

SAT Linear Equations in Two Variables Question 77 | Free SAT Prep | Aniko

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Question 77·Medium·Linear Equations in Two Variables

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A local charity sold T-shirts and coffee mugs to raise funds, earning a total of $2,316. The relationship is modeled by the equation $18t + 12m = 2,316$ , where $t$ is the number of T-shirts sold and $m$ is the number of coffee mugs sold. If the charity sold $70$ coffee mugs, how many T-shirts did it sell?

Your answer

(Express the answer as an integer)

For linear equations in two variables where one variable’s value is given, substitute the known value into the equation and simplify to get a one-variable equation. Then isolate the remaining variable by performing inverse operations step by step (usually subtracting the constant term, then dividing by the coefficient). Keep track of what each number represents (money vs. quantity) to avoid stopping early or confusing variables.

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Use the given equation

You are given $18t + 12m = 2316$ and told that $m = 70$ . Which variable is known, and which variable do you need to find?

Substitute the known value

Replace $m$ with $70$ in the equation. What expression do you get instead of $12m$ ?

Isolate the T-shirt term

After substituting, move the mug term to the other side by subtracting it from 2316. What is $2316$ minus the mug total?

Solve for $t$

Once you have an equation of the form $18t = \text{(number)}$ , what operation will isolate $t$ ?

Desmos Guide

Use Desmos to compute $t$ directly

In Desmos, type the expression (2316 - 12*70)/18 and press Enter. The value that Desmos outputs is the number of T-shirts $t$ .

Step-by-step Explanation

Identify what is known and what is unknown

The equation $18t + 12m = 2316$ models the money raised:

$t$ is the number of T-shirts.
$m$ is the number of coffee mugs. You are told that $m = 70$ and you need to find $t$ .

Substitute the known value into the equation

Replace $m$ with $70$ in the equation $18t + 12m = 2316$ :

18t + 12(70) = 2316

Now simplify $12(70)$ .

Simplify and isolate the T-shirt term

Compute the mug total:

12 \times 70 = 840

So the equation becomes:

18t + 840 = 2316

Subtract 840 from both sides to isolate the $18t$ term:

18t = 2316 - 840 = 1476

Solve for the number of T-shirts

Now divide both sides by 18 to solve for $t$ :

\frac{18t}{18} = \frac{1476}{18}

t = 82

So, the charity sold 82 T-shirts.

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Desmos Guide

Step-by-step Explanation

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Desmos Guide

Step-by-step Explanation