Maths Problem 8

Question

When opening her piggy bank, Mary noticed that she had 104 coins made up entirely of 20c and 5c coins that totalled exactly $10. How many of each type of coins did she have?

Answer 1

I believe you meant 10 cent coins because there is no coin that is worth 20 cents by itself. This means you must give a combination of coins to get 20 cents.

 

 

5 cents is the same as $0.05

10 cents is the same as $0.10

 

 

Since we need to find the number of each type of coin, we set variables for them.

 

Let the number of 5 cent coins = x

Let the number of 10 cent coins = y

 

 

Next, write equations that represent the information.

 

x + y = 104             eq1

 

0.05x + 0.10y = 10             eq2

 

 

Substitute eq1 into eq2.  We will get eq2 in terms of x.

 

0.05x + 0.10(104 - x) = 10

 

Solve for x.

 

 

0.05x + 10.4 - 0.10x = 10

 

-0.05x + 10.4 = 10

 

-0.05x = -0.4

 

        x = 8

 

Substitute this value of x into eq1 to solve for y.

 

y = 104 - 8

 

y = 96

 

 

Mary has 8 coins that are worth 5 cents and 96 coins that are worth 10 cents.