Write a system of equations that models the equation.

Question

You have a jar of pennies and quarters. You want to choose 15 coins that are worth exactly $4.35. Write and solve a system of equations that models the situation.

Answer 1

15 coins (pennies and quarters) worth exactly $4.35

p + q = 15

.01p + .25q = 4.35

multiply 1st equation by 1/4= .25 or divide by 4

p/4 + q/4 = 15/4

.25p + .25q = 15(.25) = 3.75

subtract from 2nd equation to eliminate one variable and get

p = negative 2 1/2 pennies

q = 17 1/2 quarters

q p total value

15 0 $3.75 = maximum possible value of 15 such coins

14 1 3.5 + .01 = 3.51

no solution. DNE Does Not exist

null Set {}

no positive real solution

but a mixed negative/positive real solution, not mathematically imaginary, but negative coins are in real life imaginary

17 1/2 quarters = 4.375

-2.5 pennies = -025

add them: 4.35