WAEC 2019 · Paper 2 · Q3

(a)
Ali, Musah and Yusif shared ₦420,000.00 in the ratio $3 : 5 : 8$ respectively. Find the sum of Ali's and Yusif's shares.
(b)
Solve: $2\left(\frac18\right)^x = 32^{x - 1}$ .

Worked solution (try it first)

(a)

The ratio has $3 + 5 + 8 = 16$ parts, so one part is $\frac{420\,000}{16} = 26\,250$ .
Ali gets $3 \times 26\,250 = ₦78,750$ and Yusif $8 \times 26\,250 = ₦210,000$ .
Together: ₦288,750.

(b)

Write both sides as powers of 2: $2 \times (2^{-3})^x = 2^{1 - 3x}$ and $32^{x - 1} = 2^{5(x - 1)} = 2^{5x - 5}$ .
So $1 - 3x = 5x - 5$ , $8x = 6$ and $x = \frac34$ .

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