Question

Emily has 8 coins in her purse totaling 50 cents. The only kinds of coins she has are nickels and dimes. How many nickels does Emily have?

Answer 1

5x + 10y = 50
x + y = 8

x = 8 - y
5*(8-y) + 10y = 50
40 - 5y + 10y = 50
10y - 5y = 50 - 40
5y = 10
y = 2

x + y = 8
x + 2 = 8
x = 8 - 2
x = 6

She has 6 nickels and 2 dimes

Answer 2

The number of nickels that Emily has is 6 nickels.

• Let the number of nickels be n.

• Let the number of dimes be d.

Given the following data:

• Number of coins = 8 coins

• Total value of coins = 50 cents.

Scientific data:

• 1 nickel = 5 cents.

• 1 dime = 10 cents.

To determine the number of nickels that Emily has:

How to solve a word problem.

Translating the word problem into an algebraic expression, we have;

$5n +10d=50$   ....equation 1.

$n+d=8$    .....equation 2.

From equation 2, we have:

$d=8-n$   ...equation 3.

Substituting eqn. 3, into eqn. 1, we have:

$5n +10(8-n)=50\\\\5n+80-10n=50\\\\80-5n=50\\\\5n=80-50\\\\5n=30\\\\n=\frac{30}{5}$

n = 6 nickels.

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