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Algebra Level pending

In a certain country, the cost of a baseball and a baseball glove is 1540. The cost of the baseball is 440 less than the cost of the baseball glove. What is the cost of the baseball?

Note: All costs are in local currency.

540 890 550 620

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2 solutions

Munem Shahriar
Mar 16, 2018

If x x is the cost of the baseball and y y is the cost of the baseball glove, we can write:

{ x + y = 1540 . . . . . ( 1 ) x y = 440 . . . . . ( 2 ) \large \begin{cases} x + y & = 1540~~~~~~ .....(1) \\ x - y & = -440 ~~~~~~ .....(2) \\ \end{cases}

after ( 1 ) + ( 2 ) , (1) + (2), we get,

x + x = 1540 + ( 440 ) 2 x = 1540 440 x = 1100 2 x = 550 . \begin{aligned} x + x & = 1540 + (-440) \\ 2x & = 1540 - 440 \\x & = \dfrac{1100}2 \\ x & = \boxed{550}. \\ \end{aligned}

let b = cost of baseball and g = cost of baseball glove, then we have the two equations

b + g = 1540 (eq. 1)

b = g - 440 (eq. 2)

from (eq. 2), we get

g = b + 440

substitute the above in (eq. 1), we have

b + b + 440 = 1540

2b = 1100

b = 550 (answer)

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