Step 3: Use equation(1)to expressbin terms ofj
b=j+ 2Step 4: Substitute into equation(2)
b+j= 14
(j+ 2) +j= 14Step 5: Rearrange and solve forj
2 j= 14 2
= 12
)j= 6Step 6: Substitute the value forjback into equation(1)and solve forb
b=j+ 2
= 6 + 2
= 8Step 7: Check that the solution satisfies both original equations
Step 8: Write the final answer
Bongani got 8 for his test and Jane got 6.
Worked example 13: Solving word problemsQUESTION
A fruitshake costs R 2,00 more than a chocolate milkshake. If 3 fruitshakes and 5 chocolate milkshakes cost
R 78,00, determine the individual prices.
SOLUTION
Step 1: Assign variables to the unknown quantities
Let the price of a chocolate milkshake bexand let the price of a fruitshake bey.
Step 2: Set up a system of equations
y=x+ 2 : : :(1)
3 y+ 5x= 78 : : :(2)Chapter 4. Equations and inequalities 91