SOLUTION: Emma paid the $11.14 bill for her lunch with 248 coins consisting of pennies, nickels, and dimes. If the number of nickels and dimes was equal to the number of pennies, then how ma

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Question 1039480: Emma paid the $11.14 bill for her lunch with 248 coins consisting of pennies, nickels, and dimes. If the number of nickels and dimes was equal to the number of pennies, then how many coins of each type did she use?
Answer by Aldorozos(172) (Show Source):
You can put this solution on YOUR website!
x = number of pennies
y = number of nickels
z = number of dimes
xp + y(5p) + z(10p) = 1114 we know that 11.14 is equal to 1114 pennies. Here we have written everything in terms of pennies
y+z = x according to the problem
x+y+z = 248 according to the problem. We can replace y+z here with x
x+x = 248 Therefore 2x = 248 this gives us x=124 which means we have 124 pennies. Now we have to find the number of dimes and nickels.
124+ 5y +10z = 1114
Simplifying this problem we have
5y +10z = 990 and we already know y+z = 124 = x
Now we have two equations and two unknowns
5y +10z = 990 and y+z = 124 If y+z = 124 then y = 124 - z. We replace y in the first equation with z
5(124-z) + 10z = 990 and therefore z = 74. If z is 74 y has to be 50 since y = 124-z
To see if this is correct we can calculate
124 + 5 (50) + 10 (74) if the total number is 1114, then we have solved the problem correctly.