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

Answer:

Jennifer has 7 quarters

Step-by-step 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