Question

A pile of 70 coins ,consisting of only nickels and dimes, is worth 4 dollars and 60 cents. Find the number of nickels.

Answer 1

There are 48 nickels in the pile.

Step-by-step explanation:

Given,

Number of coins = 70

Worth of coins = $4.60 = 4.60*100 = 460 cents

1 nickel = 5 cents

1 dime = 10 cents

Let,

x be the number of nickels

y be the number of dimes

According to given statement;

x+y=70          Eqn 1

5x+10y=460   Eqn 2

Multiplying Eqn 1 by 10

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

Subtracting Eqn 2 from Eqn 3

$(10x+10y)-(5x+10y)=700-460\\10x+10y-5x-10y=240\\5x=240$

Dividing both sides by 5

$\frac{5x}{5}=\frac{240}{5}\\x=48$

There are 48 nickels in the pile.

Keywords: linear equation, elimination method

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