word problem

Question

Suppose Maria has 160 coins consisting of pennies, nickels and dimes, number of nickels she has is 10 less than twice the number of pennies, the number of dimes she has is 22 less than 3 times the number of pennies, How many coins of each kind does she have?

Answer 1

set up equations for each statement:  p+n+d=160, n=2p-10 and d=3p-22

substitute 2nd and 3rd equations into the first

so p+(2p-10)+(3p-22)=160

combine like terms on the left 6p-32=160

add 32 to both sides and 6p=192

divide both sides by 6 and p=32

put this into 2nd and 3rd equations

so, n=2(32)-10 or n=54 and d=3(32)-22 or d=74

p=32, n=54 and d=74