Everything Maths Grade 10

Step 3: Substitute equation(1)into(2)

3 (x+ 2) + 5x= 78

Step 4: Rearrange and solve forx

3 x+ 6 + 5x= 78

8 x= 72

)x= 9

Step 5: Substitute the value ofxback into equation(1)and solve fory

y=x+ 2

= 9 + 2

= 11

Step 6: Check that the solution satisfies both original equations

Step 7: Write final answer

One chocolate milkshake costs R 9,00 and one fruitshake costs R 11,00.

Worked example 14: Solving word problems

QUESTION

The product of two consecutive negative integers is 1122. Find the two integers.

SOLUTION

Step 1: Assign variables to the unknown quantities

Let the first integer benand let the second integer ben+ 1

Step 2: Set up an equation

n(n+ 1) = 1122

Step 3: Expand and solve forn

n^2 +n= 1122

n^2 +n 1122 = 0

(n+ 34) (n33) = 0

)n= 34

orn= 33

92 4.5. Word problems