algebra math problem

Question

Suppose that Maria has 130 coins consisting of pennies, nickels, and dimes. The number of nickels she has is 13 less than twice the number of pennies; the number of dimes she has is 25 less than three times the number of pennies. How many coins of each kind does she have?

Answer 1

Let P be the number of pennies, N be the number of nickels, and D be  the number of dimes.

 

Then equation (1) is  P + N + D = 130, and

 

equation (2) is N = 2*P -13, and 

 

equation (3) is D= 3*P -25

 

Let's begin by substituting the values of N in equation 2 and D in equation 3 into equation 1, giving us

 

P + 2*P -13 + 3*P -25 = 130

combining like terms gives us

6*P-38=130 or 6*P= 130+38=168

P = 168/6 = 28

N = 2*P -13 = 2*28-13 =43

D = 3*P -25 =  3*28-25 = 59

 

Therefore the number of pennies is 28, the number of nickels is 43, and the number of dimes is 59