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Flashcards: Solving Systems of Equations in Word Problems

Blin and Alex raised a total of $240,000 for a charity. If Blin raised $60,000 more than Alex did, how much money did Blin raise?

$180,000

$120,000

$150,000

$100,000

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Flashcards: Solving Systems of Equations in Word Problems

Blin and Alex raised a total of $240,000 for a charity. If Blin raised $60,000 more than Alex did, how much money did Blin raise?

Your answer:

$180,000

Your answer:

$120,000

Your answer:

$100,000

Correct answer:

$150,000

Explanation:

This problem provides you with a classic SAT Systems of Equations setup. You're given the sum of two entities - here that's Blin's Total + Alex's Total = $240,000 - and a relationship between those two entities. Here that's Blin raised $60,000 more than Alex did.

The sum equation is generally straightforward; you can express that as B + A = 240,000. For the relationship equation, you can say that Blin's total is $60,000 more than Alex's, which translates to B = 60,000 + A.

Now you have two equations:

B + A = 240,000

B = 60,000 + A

This structure sets up well for Substitution; you already have B in terms of A, so you can plug in the second equation for the first:

(60,000 + A) + A = 240,000

60,000 + 2A = 240,000

2A = 180,000

A = 90,000

Of course, at this point you need to check whether you solved for the proper variable. The question asks you about Blin's total, not Alex's, so you need to add $60,000 to get to Blin's total of $150,000. Then check your work: does Blin's total of $150,000 plus Alex's total of $90,000 arrive at the sum we know to be $240,000? It does, so you can confidently choose $150,000.

Flashcards: Solving Systems of Equations in Word Problems

Judy and Nancy participated in a walk-a-thon to raise money for charity. They combined for 42 total miles between them, with Judy walking twice as many miles as Nancy. How many miles did Nancy walk?

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Flashcards: Solving Systems of Equations in Word Problems

Judy and Nancy participated in a walk-a-thon to raise money for charity. They combined for 42 total miles between them, with Judy walking twice as many miles as Nancy. How many miles did Nancy walk?

Your answer:

Correct answer:

Explanation:

This problem provides you with a classic SAT Systems of Equations setup: you get a sum equation about a combined total of two entities, and then an equation that gives a relationship between the two. Here you know that Judy and Nancy combined for 42 miles, which you can turn into an equation as:

J + N = 42

Then you're told that Judy walked twice as many miles as Nancy did. That equation is J = 2N (be careful about putting the two in the wrong spot - it's best to think about "what do I have to do to Nancy's total to make it equal Judy's?? You'd have to double it to catch up, so twice Nancy's total is what it takes to equal Judy's --> J = 2N).

Now you can substitute the second equation for the first. If you plug in 2N where the J appears in the first, you have:

2N + N = 42

3N = 42

N = 14

And since this problem asks you for Nancy's total, you have it: Nancy walked 14 miles.

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Flashcards: Solving Systems of Equations in Word Problems

Flashcards: Solving Systems of Equations in Word Problems

Flashcards: Solving Systems of Equations in Word Problems

Flashcards: Solving Systems of Equations in Word Problems

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All SAT Mathematics Resources

Flashcards: Solving Systems of Equations in Word Problems

Flashcards: Solving Systems of Equations in Word Problems

Flashcards: Solving Systems of Equations in Word Problems

Flashcards: Solving Systems of Equations in Word Problems

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