Answer:
Andre has more money than Bob. If Andre gave Bob $20, they would have the same amount. While if Bob gave Andre $22, Andre would then have twice as much as Bob. How much does each one actually have?
Step-by-step explanation:
Here is the first sentence:
"If Andre gave Bob $20, they would have the same amount."
Algebraically:
1) x − 20 = y + 20.
(Andre -- x -- has the same amount as Bob, after he gives him $20.)
Here is the second sentence:
"While if Bob gave Andre $22, Andre would then have twice as much
as Bob."
Algebraically:
2) x + 22 = 2(y − 22).
(Andre has twice as much as Bob -- after Bob gives him $22.)
To solve any system of two equations, we must reduce it to one equation in one of the unknowns. In this example, we can solve equation 1) for x --
x − 20 = y + 20
implies x = y + 40
-- and substitute it into equation 2):
y + 40 + 22 = 2(y − 22).
That is,
y + 62 = 2y − 44,
y − 2y = − 44 − 62,
according to the techniques of Lesson 9,
−y = −106
y = 106.
Bob has $106. Therefore, according to the exression for x, Andre has
106 + 40 = $146.
I hope this helps u! :D
