Question

Suppose that maria has 150 coins consisting of pennies, nickels, and dimes. the number of nickels she has is 14 less than twice the number of pennies; the number of dimes she has is 22 less than three times the number of pennies. how many coins of each kind does she have?

Answer 1

Let p, n, d represent the number of pennies, nickels, and dimes respectively. The problem statement tells us
.. p +n +d = 150
.. 2p -n = 14
.. 3p -d = 22
Add these three equations to find the number of pennies.
.. (p +n +d) +(2p -n) +(3p -d) = 150 +14 +22
.. 6p = 186
.. p = 31
.. n = 2*31 -14 = 48
.. d = 3*31 -22 = 71

Maria has 31 pennies, 48 nickels, and 71 dimes.