Question

Construct a word problem simultaneous linear equations in two variable.that the value of one variable will be 18

Answer 1

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?

Solution. Let x be the amount of money that Andre has. Let y be the amount that Bob has.

Always let x and y answer the question -- and be perfectly clear about what they represent!

Now there are two unknowns. Therefore there must be two equations. (In general, the number of equations must equal the number of unknowns.) How can we get two equations out of the given information? We must translate each verbal sentence into the language of algebra.

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.