SOLVING LINEAR EQUATIONS
1.The total weekly wages for 12 artisans and 4 apprentices are sh.5600. If the number of artisans is
increased to 15 and that of apprentices to 9, the total weekly wages are sh.7800. Calculate the weekly
wage for an artisan
Answer
Let x represent the weekly wage of an artisan and let y represent the weekly wage of an
apprentice
We will form two equations
12x + 4y = 5600………..(i)
15x + 9y = 7800………..(ii)
Step 2:take one of the equations and simplify it as follows..
4y= 5600 – 12x
y= 1400 – 3x
Step 3: take the other equation and replace the y with the RHS of the simplified equation
15x + 9(1400 – 3x)= 7800
Step 4: open the bracket in step 3
15x + 12600 – 27x = 7800
Step 5: put the like terms together
15x – 27x = 7800 – 12600
12x = - 4800
Step 6: Divide both sides by negative 12 to get the value of x
x = 400
Step 6: to find the value of y replace the new value of x in any of the original equations
12x + 4y = 5600
12(400) + 4y = 5600
4800 + 4y = 5600
4y = 5600 – 4800
4y = 800
y= 200
Answer: Weekly wages for artisans will be 400
1.The total weekly wages for 12 artisans and 4 apprentices are sh.5600. If the number of artisans is
increased to 15 and that of apprentices to 9, the total weekly wages are sh.7800. Calculate the weekly
wage for an artisan
Answer
Let x represent the weekly wage of an artisan and let y represent the weekly wage of an
apprentice
We will form two equations
12x + 4y = 5600………..(i)
15x + 9y = 7800………..(ii)
Step 2:take one of the equations and simplify it as follows..
4y= 5600 – 12x
y= 1400 – 3x
Step 3: take the other equation and replace the y with the RHS of the simplified equation
15x + 9(1400 – 3x)= 7800
Step 4: open the bracket in step 3
15x + 12600 – 27x = 7800
Step 5: put the like terms together
15x – 27x = 7800 – 12600
12x = - 4800
Step 6: Divide both sides by negative 12 to get the value of x
x = 400
Step 6: to find the value of y replace the new value of x in any of the original equations
12x + 4y = 5600
12(400) + 4y = 5600
4800 + 4y = 5600
4y = 5600 – 4800
4y = 800
y= 200
Answer: Weekly wages for artisans will be 400
