Word Problems on Algebraic Fractions

David and Doyin share #380.00 in such a way that 1/5 of David’s share is equal to 4/5 of Doyin’s. Find the shares. (Source: MM P114 Ex F Q9)

Solution

Let David’s share = V

Let Doyin’s share = Y

i.e. from the question, David’s share plus Doyin’s share = #380.00

i.e. V + Y = #380.00 — 1

Make Y the subject of the formula in equ (1)

i.e. Y = #380.00 – V — 2

1/5 of David’s share = 1/5 x V        — 3

4/5 of Doyin’s share = 4/5 x Y        — 4

In the question, the fraction of David’s share is equal to the fraction of Doyin’s share.

i.e. 1/5 x V = 4/5 x Y — 5

Cross multiply (CRM)

i.e. 1 x V x 5 = 5 x 4 x Y

i.e. 5V = 20Y — 6

Divide both sides (DBS) by 5

i.e. 5V/5 = 20Y/5

i.e. V = 4Y      — 7

Substitute the value of V in equ (7) into equ (2)

i.e. Y = #380.00 – 4Y           — 8

Collect like terms (CLT)

i.e. Y + 4Y = #380.00

i.e. 5Y = #380.00

Divide both sides (DBS) by 5

i.e. 5Y/5 = #380.00/5

Therefore, Y = #76.00

Substitute the value of Y into equ (7)

i.e. V = 4 x #76.00

Therefore, V = #304.00

Note that you can also substitute the value of Y into equ (2) to solve for the value of V.

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