# 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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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

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$

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.