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There were 3 friends, A, B and C, sharing the cost of a toy.
The ratio of A's share to the total of B and C is 1:3.

The ratio of B's share to the total of A and C is 1:5

C spent $80 more than B. Find the cost of the toy.

 Mar 27, 2022
 #1
avatar+1361 
+2

Write as a system of 3 equations: 

 

\(3a = b+c\)  (Equation 1)

\(5b = a+c\)  (Equation 2)

\(c=80+b\)  (Equation 3)

 

Sub in (Equation 3) into (Equation 2):  \(5b = a+b+80\)

Simplify:  \(b = {a \over 4}+20\)

Now, sub what we found for b, and (Equation 3) into (Equation 1): \(3a= {a \over 4} +20+80+ {a \over 4} +20\)

Solving, we find \(a = 48\)

Subbing the value of \(a\) we just found and (Equation 3) into (Equation 2), we get: \(5b = 48+80+b\)

Solving, we find \(b = 32\)

Plugging in what we found for the value of \(b\) into (Equation 3), we find that \(c = 112\).

Now do \(a + b+c\) to find your answer. 

 Mar 27, 2022
 #2
avatar
+1

3a + b + c -------------- (1)

5b = a + c -------------- (2)

c = 80 + b -------------- (3)

put c = 80 + b in equation (2)

   5b = a + b + 80

 5b = b = a + 80 => 4b = a + 80

b = \( {a \over 4}\) + \( {80 \over 4}\) = \( {a \over 4}\) + 20

put b = \( {a \over 4}\) + 20 and c = 80 + b in Eq (1)

3a = \( {a \over 4}\) + 20 + 80 + \( {a \over 4}\) + 20

3a = \( {a \over 4}\) + \( {a \over 4}\) + (80 + 20 + 20)

3a = 2 * \( {a \over 4} \) + 120 => 3a - \( {2a \over 4}\) = 120

\( {12a - 2a \over 4}\) = 120 => \( {10a \over 4}\) = 120 => a = \( {120 * 4 \over 10}\) = 48

put a = 48 and c = 80 + b in equation (2)

we get 5b = 48 + 80 + b => 5b - b = 128

4b = 128 => b = \( {128 \over 4}\) = 32

pluf the value of b in equation (3) we get

c = 80 + 32 = 112

Now do a + b + c to find your answer

a = 48, b = 32, c = 112

80     a + b + c = 48 + 32 + 112

  = 192 

80  a + b + c = 192 (Ans)

Guest Mar 28, 2022
 #3
avatar+36416 
+1

From BB:

a = (b+c)/3     and   a = 5b - c       <======equate

 

 5b-c = (b+c)/3

   re-arrange to    16b - 4c = 0         sub in  c = 80 + b

                             16 b - 4(80+b) = 0            results in    b = 32      then   c = 112      then a = 48      summed = 192

 Mar 28, 2022

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