Divide 102 dollars among 3 boys. A,B, and C, so that A gets twice as much as B and C gets 1 1/2 times as much as A. How much does each boy get?
Boy A gets $34, boy B gets $17 and boy C gets $51 and this can be determined by forming the linear equation and by using the arithmetic operations.
Given :
It is given that A gets twice as much as B, that is:
A = 2B
\(\rm 0.5 A = B\) ----- (1)
It is also given that C gets 1.5 times as much as A, that is:
\(\rm C = 1.5 A\) ------ (2)
Given that the total amount is $102, that is:
A + B + C = 102 --- (3)
Now, put the value of B and C in equation (3).
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3A = 102
A = $34
Now, put the value of A in equations (1) and (2).
\(\rm B = 0.5\times 34\)
B = $17
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C = $51
Boy A gets $34, boy B gets $17 and boy C gets $51.
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