If x + y = $22 and the price of x was 20% higher than the price of y, what does y equal?

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Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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If x + y = $22 and the price of x was 20% higher than the price of y, what does y equal? 

Here are the equations we have: 

x + y = 22

1.2x = y 

since we want y: 

(y/1.2) + y = 22

y = 10

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

The first answer given above is correct, but the method of arriving at the answer is not given. The following method can be used for solving all problems of this type.

Solution:

Given that x + Y = 22   ... (1)

and that X is 20% higher than price of y.

Therefore x = y + (20% 0f Y) = y + y*(20/100) = 1.2Y

Substituting this value of x in equation (1) we get:

1.2y + y = 22

Therefore: 2.2Y = 22

Therefore: Y = 22/2.2 = 10

Substituting this value of y in equation 1 we get

x +10 = 22

Therefore: x = 22 - 10 = 12

Answer: X = 12$ and y = 10$

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

x+y=$22.......... (1)

x is 20% higher than the price, y. This means x is (20% of y)+y or x=(20/100)*y + y= (0.2+1)y=1.2y or

x=1.2y .............(2)

(1) and (2) are the two simultaneous equations which can be solved either by substitution method or by elimination method. We use thesubstitution method.

Therefore, the equaion x+y=$22 could be writtten using x=1.2 like:

1.2y+y=$22 or

2.2y=$22 or

y=$22/2.2=$10, the required solution.

Therefore, y=$10 is the required solution

Now,put y=10 in (2) to get the value of x:

x=1.2y =1.2*$10=$12.

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