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3 years ago

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Mathematics

1 answer:

allsm [11]3 years ago

4 0

Answer:

Jennifer has 7 quarters

Step-by-step explanation:

<u><em>The correct question is</em></u>

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

$y=3(11)=33$

The number of pennies is 11

The number of nickels is 33

The number of quarters is 7

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Step-by-step explanation:

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This image has the step by step solution