A trader sells big, medium, and small yams. 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 sale for that day amounted to GH$1372.00. The problem asks to find the number of big, medium, and small yams sold on that day.

1. Problem Description

A trader sells big, medium, and small yams. 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 sale for that day amounted to GH$1372.

0

0. The problem asks to 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.

The problem provides the following information:

$m = b + 15$

$s = 2m$

The price of each big yam is GH$12.00, so the total revenue from big yams is$12b$.

The price of three medium yams is GH$20.00, so the price of each medium yam is$20/3$. The total revenue from medium yams is$(20/3)m$.

The price of five small yams is GH$18.00, so the price of each small yam is$18/5$. The total revenue from small yams is$(18/5)s$.

The total sale for the day is GH$1372.00, so

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

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

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

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

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

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

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

Multiply by 15 to eliminate fractions:

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

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

$388b = 17460$

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

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

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

Therefore, the number of big yams sold is

4

5. The number of medium yams sold is

6

0. The number of small yams sold is

1

2

0.

3. Final Answer

i. Number of big yams: 45

ii. Number of medium yams: 60

iii. Number of small yams: 120