SAT Linear Equations in Two Variables Question 25 | Free SAT Prep | Aniko

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Question 25·Easy·Linear Equations in Two Variables

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At a school fundraiser, bracelets cost $2 each and necklaces cost $5 each. The equation

2x + 5y = 50

represents the total amount of money, in dollars, collected from selling $x$ bracelets and $y$ necklaces. If $4$ necklaces are sold, how many bracelets are sold?

For SAT word problems that give a linear equation and then specify one variable, plug the given value into the equation immediately and simplify to a one-variable equation. Then solve step by step using inverse operations (undo addition/subtraction first, then multiplication/division). Finally, check by plugging your result back into the original context to ensure the total (like money or distance) matches the problem description.

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Use the given equation

You are given an equation that relates bracelets ( $x$ ) and necklaces ( $y$ ) to the total money collected. Focus on that equation: $2x + 5y = 50$ .

Substitute the known value

You are told that 4 necklaces are sold. Replace $y$ in the equation with 4, then simplify.

Solve the one-variable equation

After substituting $y=4$ , you will have an equation in terms of $x$ only. Use inverse operations (undo addition, then undo multiplication) to solve for $x$ .

Desmos Guide

Enter the equation with the known value of y

In Desmos, type 2x + 5(4) = 50 (this substitutes 4 for $y$ ). Desmos will treat this as an equation in $x$ only.

Solve or inspect the solution for x

Click on the equation or use the Desmos solver feature (if available) to find the value of $x$ that makes the equation true. The $x$ -value you see is the number of bracelets sold.

Step-by-step Explanation

Substitute the given number of necklaces

We are told that $y=4$ necklaces are sold. Substitute $y=4$ into the equation:

2x + 5(4) = 50

This replaces $y$ with the known value so the equation now has only one variable, $x$ .

Simplify the equation

Now simplify $5(4)$ and rewrite the equation:

$5(4) = 20$

So the equation becomes

2x + 20 = 50

Isolate the term with $x$

To isolate the $2x$ term, subtract 20 from both sides of the equation:

2x + 20 - 20 = 50 - 20 \\[0.7em] 2x = 30

Solve for $x$ and interpret the result

Now divide both sides by 2 to solve for $x$ :

\frac{2x}{2} = \frac{30}{2} \\[0.7em] x = 15

So, 15 bracelets were sold.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation