Question

One catcher's mitt and 10 outfielder's gloves cost $239.50. How much does each item cost if 1 catcher's mitt and 5 outfielder's gloves cost $134.50?

A The cost of a catcher's mitt is $29.50 and an outfielder's glove is $21.00.
B The cost of a catcher's mitt is $28.80 and an outfielder's glove is $21.07.
C The cost of a catcher's mitt is $28.50 and an outfielder's glove is $21.10.
D The cost of a catcher's mitt is $31.50 and an outfielder's glove is $20.60.

Answer 1

Make an equation for each statement with x being catcher's mitts and y being outfielder's gloves.

x + 10y = 239.50 and x + 5y = 134.50

Multiply the second equation through by -1 giving -x - 5y = -134.50

Combine the equations vertically

x + 10y = 239.50
-x - 5y = -134.50

giving

5y = 105
y = 21

Now substitute for y:
x + 10(21) = 239.50
x + 210 = 239.50
x = 29.50

Thus, Catchers mitts $29.50 and outfielder's gloves are $21