Question 180229: System of Equations: John is going to Costa Rica over Spring Break. Before his trip, he purchases 10 travelers checks in denominations of $20, $50 and $100, totaling $370. He has twice as many $20 checks as $50 checks. How many of each type of denomination of travelers checks does he have?
Answer by MathTherapy(10551)   (Show Source):
You can put this solution on YOUR website! Let the amount of $50 checks be f,
Then the amount of $20 checks is 2f
Let the amount of $100 checks be o
Therefore, 2f + f + o = 10, or 3f + o = 10
Then 2f(20) + f(50) + o(100) = 370, or 40f + 50f + o(100) = 370, or 90f + 100o = 370
3f + o = 10 ----------- (i)
90f + 100o = 370 --------- (ii)
-90f - 30o = - 300 -------- (iii) Multiply eq (i) by – 30:
70o = 70 Add eq (iii) & eq (ii)
o = 1
Substituting 1 for o in eq (i), we get: 3f + 1 = 10
3f = 9
f = 3
Therefore, there are 2f, or 2(3) $20 checks, or 6 $20 checks = $120
There are f or 3 $50 checks = $150
There is o or 1 $100 check = $100
Checking:
Altogether, there are 6 + 3 + 1 = 10 checks, and these checks add up to $120 + $150 + $100 = $370.
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