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Question 220484: You have quarters, dimes and nickels with a total value of 500 cents or $5.00. The number of nickels is twice the number of quarters. The number of dimes is four less than the number of quarters.
a. Explain why the expression 5(2q) represents the value of the nickels if q represents the number of quarters. How can you simplify the expression?
b. Write and solve an equation to find the number of each type of coin.
We have tried to solve for the last 30 minutes. I would like to share our work, but there was copious amounts of it.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You have quarters, dimes and nickels with a total value of 500 cents or $5.00. The number of nickels is twice the number of quarters.
saThe number of dimes is four less than the number of quarters.
a. Explain why the expression 5(2q) represents the value of the nickels if q represents the number of quarters.
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How can you simplify the expression?
(unit value)*(# of units) = total value:
So, 5(2q) = 10q is the total value of the quarters
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b. Write and solve an equation to find the number of each type of coin.
Value Eq.: 25q + 10d + 5n = 500 cents
Quantity Eq: n = 2q
Quantity Eq: d = q-4
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Substituting you get:
Value Eq: 25q + 10(q-4) + 5(2q) = 500
25q + 10q-40 + 10q = 500
45q -40 = 500
45q = 540
q = 12 (# of quarters)
n = 2q = 24 (# of nickels)
d = q-4 = 8 (# of dimes)
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Cheers,
Stan H.
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