Question

8

Jennifer has $ 3.51 in change in her
piggy bank. The change consists of 51
coins inducing pennies, tickets and
quarters. If there are 3 umes as many
níckets as pennies, how many quarters
does she have?
Enter your answer on the
answer document,

Answer 1

Jennifer has 7 quarters

Explanation:

The correct question is

Jennifer has $ 3.51 in change in her piggy bank. The change consists of 51 coins inducing pennies, nickels and quarters. If there are 3 times as many nickels as pennies, how many quarters does she have?

Remember that

`1\ penny=\$0.01\\1\ nickel=\$0.05\\1\ quarter=\$0.25`

Let

x ----> the number of pennies

y ---> the number of nickels

z ---> the number of quarters

we know that

`x+y+z=51` -----> equation A

`0.01x+0.05y+0.25z=3.51` ----> equation B

`y=3x` ---> equation C

substitute equation C in equation A and equation B

`x+3x+z=51`

`4x+z=51` -----> equation D

`0.01x+0.05(3x)+0.25z=3.51`

`0.16x+0.25z=3.51` ----> equation E

we have

`4x+z=51` -----> equation D

`0.16x+0.25z=3.51` ----> equation E

Solve the system of equations D and E by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (11,7)

x=11,z=7

see the attached figure

Find the value of y

`y=3(11)=33`

so

The number of pennies is 11

The number of nickels is 33

The number of quarters is 7