Can someone help me with this word problem?

Question

The profit on a blue car is $10 more than the profit on a white car, and the profit on a red car is $7 less than the profit on a white car. If the profit on two red cars is $2 less than the profit on one blue car, what is the profit on a blue car? My answer is $25 but it doesn't match with any answer in the answer box.

 

Answer 1

Let r, b and w profits from red, blue and white cars respectively.

 

From the given conditions we get: b = w + 10 ..(1), r = w -7  ...(2)and 2r = b -2 ..(3)

 

Let's eliminate w from equation (1) and (2):

  b - 10 = w (from equation 1) = r+7 (from eqn 2)

 

ie b - 10 = r + 7, or  r = b -10 -7 = b -17 or  multiplying both sides by 2,  2r = 2*(b-17) = 2b -34  -- (4)

 

If we equate  2r from (3) and (4), we get 2b -34 = b -2

 

Subtract  b and  and add 34 on both sides, we get 2b -34 -b +34 = b -2 -b +34 or b = 32.

 

Answer is 32.

 

Check b = 32, w =22, r = 15, 2r = 2*15 =30= 32 -2 = b-2.

Answer 2

B=profit on a blue car

W=profit on a white car

R=profit on a red car

B=W+10

R=W-7

2R=B-2

subtract the equation 2 from equation 1

B=W+10

R=W-7

B-R=W-W+10-(-7)

B-R=17

2R=B-2 is equation 3

solve for B

2R+2=B

substitute 2R+2 for B in B-R=17

2R+2-R=17

R+2=17

R=17-2

R=15

use equation 2

R=W-7

substitute

15=W-7

15+7=W

W=22

use equation 1

B=W+10

substitute

B=22+10

B=$32 profit on a blue car