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# Help

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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
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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
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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

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
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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