Question

Daniele has 33 quarters and dimes in her piggy bank. The piggy bank contains a total of $4.95. Write and solve a system of equations to find the number of dimes x and the number of quarters y. Solve the linear system by substitution.

Answer 1

Answer:the number of dimes is 22

the number of quarters is 11

Step-by-step explanation:

A dime is worth 10 cents. Converting to dollars, it becomes 10/100 = $0.1

A quarter is worth 25 cents. Converting to dollars, it becomes 25/100 = $0.25

Let x represent the number of dimes.

Let y represent the number of quarters.

Daniele has 33 quarters and dimes in her piggy bank. This means that

x + y = 33

The piggy bank contains a total of $4.95. This means that

0.1x + 0.25y = 4.95 - - - - - - - - -1

Substituting x = 33 - y into equation 1, it becomes

0.1(33 - y) + 0.25y = 4.95

3.3 - 0.1y + 0.25y = 4.95

- 0.1y + 0.25y = 4.95 - 3.3

0.15y = 1.65

y = 1.65/0.15 = 11

Substituting y = 11 into x = 33 - y, it becomes

x= 33 - 11 = 22