Question

A collection of dimes and quarters is worth $10.45. There are 70 coins in all. Find how many of each there are

Answer 1

There are 47 dimes and 23 quarters.

Step-by-step explanation:

Total amount = $10.45 = 10.45*100 = 1045 cents

Total coins = 70

1 dime = 10 cents

1 quarter = 25 cents

Let,

Dimes = x

Quarters = y

According to given statement;

x+y=70   Eqn 1

10x+25y=1045   Eqn 2

Multiplying Eqn 1 by 10;

$10(x+y=70)\\10x+10y=700\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(10x+25y)-(10x+10y)=1045-700\\10x+25y-10x-10y=345\\15y=345$

Dividing both sides by 15;

$\frac{15y}{15}=\frac{345}{15}\\y=23$

Putting y=23 in Eqn 1

$x+23=70\\x=70-23\\x=47$

There are 47 dimes and 23 quarters.

Keywords: linear equations, subtraction

Learn more about linear equations at:

• brainly.com/question/12954015
• brainly.com/question/13018923

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