A trader sells yams in three sizes: big, medium, and small. The prices are GH¢12.00 for each big yam, GH¢20.00 for three medium yams, and GH¢18.00 for five small yams. On a particular day, the number of medium yams sold was 15 more than the number of big yams sold. The number of small yams sold was twice the number of medium yams sold. The total sales for that day amounted to GH¢1372.00. Find the number of big, medium, and small yams sold on that day.

1. Problem Description

A trader sells yams in three sizes: big, medium, and small. The prices are GH¢12.00 for each big yam, GH¢20.00 for three medium yams, and GH¢18.00 for five small yams. On a particular day, the number of medium yams sold was 15 more than the number of big yams sold. The number of small yams sold was twice the number of medium yams sold. The total sales for that day amounted to GH¢1372.

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0. Find the number of big, medium, and small yams sold on that day.

2. Solution Steps

Let $b$ be the number of big yams sold.

Let $m$ be the number of medium yams sold.

Let $s$ be the number of small yams sold.

We are given that the number of medium yams sold was 15 more than the number of big yams sold, so

$m = b + 15$.

The number of small yams sold was twice the number of medium yams sold, so

$s = 2m = 2(b + 15) = 2b + 30$.

The price of each big yam is GH¢12.

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0. The price of each medium yam is GH¢20.00 /

3. The price of each small yam is GH¢18.00 /

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The total sales for the day was GH¢1372.00, so

$12b + \frac{20}{3}m + \frac{18}{5}s = 1372$.

Substitute $m = b + 15$ and $s = 2b + 30$ into the equation:

$12b + \frac{20}{3}(b + 15) + \frac{18}{5}(2b + 30) = 1372$

$12b + \frac{20}{3}b + \frac{20}{3}(15) + \frac{36}{5}b + \frac{18}{5}(30) = 1372$

$12b + \frac{20}{3}b + 100 + \frac{36}{5}b + 108 = 1372$

$12b + \frac{20}{3}b + \frac{36}{5}b = 1372 - 100 - 108 = 1164$

Multiply by 15 to clear fractions:

$15(12b) + 15(\frac{20}{3}b) + 15(\frac{36}{5}b) = 15(1164)$

$180b + 100b + 108b = 17460$

$388b = 17460$

$b = \frac{17460}{388} = 45$

Now we can find $m$ and $s$:

$m = b + 15 = 45 + 15 = 60$

$s = 2m = 2(60) = 120$

Therefore, the number of big yams sold is 45, the number of medium yams sold is 60, and the number of small yams sold is

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3. Final Answer

Big yams: 45

Medium yams: 60

Small yams: 120