The problem consists of three parts: a) Simplify the algebraic expression $5(6 - ab) + 2(-7 + 3ab)$. b) Given the equation of a straight line $3x - 2y - 6 = 0$, find the gradient and y-intercept. c) Adwoa received a commission of 20% on bread she sold, and her commission for one week was GHC 540.00. Find the total amount of bread she sold during that week and her average daily commission.

1. Problem Description

The problem consists of three parts:

a) Simplify the algebraic expression $5(6 - ab) + 2(-7 + 3ab)$.

b) Given the equation of a straight line $3x - 2y - 6 = 0$, find the gradient and y-intercept.

c) Adwoa received a commission of 20% on bread she sold, and her commission for one week was GHC 540.

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0. Find the total amount of bread she sold during that week and her average daily commission.

2. Solution Steps

a) Simplify $5(6 - ab) + 2(-7 + 3ab)$.

Expand the expression:

$5(6 - ab) + 2(-7 + 3ab) = 30 - 5ab - 14 + 6ab$

Combine like terms:

$30 - 14 - 5ab + 6ab = 16 + ab$

b) The equation of a straight line is $3x - 2y - 6 = 0$.

(i) Find the gradient of the line.

Rearrange the equation into the slope-intercept form, which is $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept.

$3x - 2y - 6 = 0$

$2y = 3x - 6$

$y = \frac{3}{2}x - 3$

The gradient of the line is $\frac{3}{2}$.

(ii) Find the y-intercept.

From the equation $y = \frac{3}{2}x - 3$, the y-intercept is $-3$.

c) Adwoa's commission is 20% and her commission for one week is GHC 540.

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0.

(i) How much bread did she sell during that week?

Let $x$ be the total amount of bread she sold. Then, 20% of $x$ is GHC 540.

0

0. $0.20x = 540$

$x = \frac{540}{0.20}$

$x = 2700$

The total amount of bread she sold is GHC

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7

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0.

(ii) Find her average daily commission.

Her weekly commission is GHC 540.

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0. There are 7 days in a week.

Average daily commission = $\frac{540}{7}$

Average daily commission $\approx$ 77.14

3. Final Answer

a) $16 + ab$

b) (i) Gradient = $\frac{3}{2}$

(ii) y-intercept = $-3$

c) (i) Amount of bread sold = GHC 2700.00

(ii) Average daily commission = GHC 77.14