Confused about how to solve a college word problem! Please help clarify, where I went wrong!

Question

Ted has a fixed amount of money in his budget for holiday gifts. He decides that his wife and his mother will receive gifts of equal value. The gift for his sister will cost half of what his mother’s gift cost, and his brother’s gift will be equal to his sister’s. He will also spend $20 on a video game for his nephew. Let T represent Ted’s total budget and x represent the value of his sister’s gift. What equation can Ted use to solve this problem?

 

 

A. T= 6x+20

B. T= x+x=2x+20

C. T = x^2 +4x+20

D. T = 3X+20

 

I tried to substitute with variables, so what I did was:

mom =x

wife= x

brother = 1/2 x

sister = 1/2 x

 

So then I had x+x+1/2x+1/2x+20= T

Then I was left with the equation 3x+20=T

 

However, I was told the answer was 6x+20 = T

 

Please explain to me, where I made a mistake at!  Thanks!!

Answer 1

Yes, Mark is on the money. The problem TELLS you that x is the value of the sister's gift. This makes the brother also x and the mom and wife each 2x.

Answer 2

The mistake is in the ascription of the variable

x represents the cost of the sister's gift.

 

Make adjustment and rewrite equation.