Question

1. 5 Burgers and 3 orders of fries cost $34. 4 Burgers and 4 orders of fries cost $32. How much does each burger and each order of fries cost?

2. A pile of 44 coins is made up of pennies, nickels, and dimes. If the pile is worth $3.07 and there are twice as many nickels as pennies, how many of each coin does the pile contain?

Answer 1

1.

a burger costs $5

an order of fries costs $3

2.

7 pennies

14 nickels

23 dimes

Explanation:

x = price of a burger

y = price of a order of fries

5x + 3y = 34

4x + 4y = 32

=>

x + y = 8

x = 8-y

5×(8-y) + 3y = 34

40 - 5y + 3y = 34

-2y = -6

y = $3

x = 8 - 3 = $5

x = number of pennies

y = number of nickels

z = number of dimes

0.01×x + 0.05×y + 0.1×z = 3.07

y = 2x

x + y + z = 44

x + 2x + z = 44

3x + z = 44

z = 44 - 3x

0.01×x + 0.05×2x + 0.1×z = 3.07

0.11×x + 0.1×z = 3.07

0.11×x + 0.1×(44-3x) = 3.07

11x + 10×(44-3x) = 307

11x + 440 - 30x = 307

-19x = -133

x = 7

y = 2×7 = 14

z = 44 - 3×7 = 44 - 21 = 23