Question 189846
A jar contains quarters and nickels. There are 25 coins in the jar, and the total value of the coins is $5.05
How many quarters and how many nickels are in the jar?

1. Define the variables:
q = number of quarters
n = number of nickels
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3. Define two more values:
{{{.25q}}} = value of the quarters, in dollars
{{{.05n}}} = value of the nickels, in dollars
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3. Since the number of quarters plus the number of nickels equals 25, set up this equation to solve:
{{{q + n = 25}}}
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4. Solve for one variable by subtracting the other from both sides:
{{{q + n - n = 25 - n}}}
{{{q = 25 - n}}}
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5. Since the value of the quarters plus the value of the nickels equals $5.05, set up this equation next:
{{{.25q + .05n = 5.05}}}
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6. Replace q with what it equals:
{{{.25(25 - n) + .05n = 5.05}}}
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7. Distribute .25:
{{{6.25 - .25n + .05n = 5.05}}}
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8. Simplify the variable terms:
{{{6.25 - .2n = 5.05}}}
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9. Subtract 6.25 from both sides:
{{{6.25 - .2n - 6.25 = 5.05 - 6.25}}}
{{{-.2n = -1.2}}}
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10. Divide both sides by -.2:
{{{(-.2n)/-.2 = (-1.2)/-.2}}}
{{{n = 6}}}
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11. With n found, q can be found by replacing it in {{{q = 25 - n}}} with what it equals:
{{{q = 25 - 6}}}
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12. Subtract and get:
{{{q = 19}}}
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13. Combine the answers with the definitions of the variables to write the answer:
“There are 19 quarters and 6 nickels in the jar.”
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14. To check:
Add 19 and 6, getting 25.
and
Multiply the value of a quarter times 19, getting $4.75, and the value of a nickel times 6, getting $.30, and add the amounts of money, getting $5.05.