Everything Maths Grade 10

SOLUTION

Step 1: Assign variables to the unknown quantities

Letbbe the number of bicycles and lettbe the number of tricycles.

Step 2: Set up the equations

b+t= 7 : : :(1)

2 b+ 3t= 19 : : :(2)

Step 3: Rearrange equation(1)and substitute into equation(2)

t= 7b

) 2 b+ 21 3 b= 19

b= 2

)b= 2

Step 4: Calculate the number of tricyclest

t= 7b

= 7 2

= 5

Step 5: Write the final answer

There are 5 tricycles and 2 bicycles.

Worked example 12: Solving word problems

QUESTION

Bongani and Jane are friends. Bongani takes Jane’s maths test paper and will not tell her what her mark is. He
knows that Jane dislikes word problems so he decides to tease her. Bongani says: “I have 2 marks more than
you do and the sum of both our marks is equal to 14. What are our marks?”

SOLUTION

Step 1: Assign variables to the unknown quantities

We have two unknown quantities, Bongani’s mark and Jane’s mark. Let Bongani’s mark beband Jane’s mark
bej.

Step 2: Set up a system of equations

Bongani has 2 more marks than Jane.
b=j+ 2 : : :(1)

Both marks add up to 14.
b+j= 14 : : :(2)

90 4.5. Word problems