Doug have 30 quarters and 15 dimes.
Step-by-step explanation:
Given,
Number of coins = 45
Worth of coins = $9.00 = 9.00*100 = 900 cents
Each quarter = 25 cents
Each dime = 10 cents
Let,
x be the number of quarters
y be the number of dimes
According to given statement;
x+y=45 Eqn 1
25x+10y=900 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=45)\\10x+10y=450\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](25x+10y)-(10x+10y)=900-450\\25x+10y-10x-10y=450\\15x=450[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}=\frac{450}{15}\\x=30[/tex]
Putting x=30 in Eqn 1
[tex]30+y=45\\y=45-30\\y=15[/tex]
Doug have 30 quarters and 15 dimes.
Keywords: linear equation, elimination method
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Doug has 30 quarters and 15 dimes.
Let
x = number of quarters
y = number of dimes
The total number of coins is 45. Therefore,
Total amount of the coins is $9. Therefore,
Therefore,
x + y = 45
0.25x + 0.1y = 9
0.1x + 0.1y = 4.5
0.25x + 0.1y = 9
0.15x = 4.5
x = 4.5 / 0.15
x = 30
y = 45 - 30
y = 15
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