Answer:
There are 24 nickels
Step-by-step explanation:
Let x represent the number of nickels
Let y represent the number of quarters
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Value Value
Type Number of of
of of each all
Coin Coin Coin Coin
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Nickels | x | $0.05 | $0.05x
Quarters | y | $0.25 | $0.25y
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Totals 28 ——— $2.20
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The first equation comes from the “Number of coins” column.
(Number of nickels) + (Number of quarters) = (total number of coins)
Equation: x + y = 28
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The second equation comes from the “value of all coins” column.
(Value of all nickels) + (Value of all quarters) = (Total value of all coins)
0.05x + 0.25y = 2.20
Remove the decimals by multiplying each term by 100:
5x + 25y = 220
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So we have the system of equations:
{x + y = 28
{5x + 25y = 202
Solve by substitution. Solve the first equation for y:
x + y = 28
y = 28 - x
Substitute (28 - x) for y in 5x + 25y = 220
5x + 25 (28 - x) = 220
5x + 700 - 25x = 220
-20x + 700 = 220
-20x = -480
x = 24
The number of nickels is 24.
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Substitute in y = 28 - x
y = 28 - (24)
y = 4
The number of quarters is 4.
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Checking:
24 nickels is $1.20 and 4 quarters is $1.00
That’s 28 coins.
Indeed $1.20 + $1.00 = $2.20
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