Problema Solution
A man has 30 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 450 cents, how many dimes and how many quarters does he have?
Answer provided by our tutors
To solve these sorts of queries you need to set up and solve a pair of simultaneous equations.
Let Q = the number of quarters and D = the number of dimes
The first equation is Q + D = 30 (there are 30 coins)
From this we can determine that Q = 30 - D. Call this Equation 1
The second equation is based on the value. As a quarter is worth 25c and a dime = 10c
25Q +10D = 450cents Call this equation 2
However we know from Equation 1 that Q = 18-D. Therefore substitute this value (18 - D) into Equation 2 which then becomes
25(30 - D) +10D = 450
Expand the bracket
750 - 25D + 10D = 450
Simplify
750 - 15D = 450
300= 15D
Therefore D = 300/15 = 20
Therefore there are 20 dimes
As D + Q = 30 and D = 20 it means Q = 10
Check
20+10 = 30 coins total
20x10c = 200c, 10 x 25c = 250c, and of course 200cents+250cents = 450cents, so correct.