Equations with brackets, decimals and fractions · Usually met around P6
Solving word problems with equations
Let x be it, find what's equal, write the equation.
How to do it
Method
Let x be it, find what's equal, write the equation
Width x: 2(x + 7) = 30, x = 8
Another way
Work backwards
30 ÷ 2 = 15, 15 − 7 = 8
In full
Step 1: let x stand for the number you want, and say what it is (let the width be x cm). Step 2: find what is equal in the story and write it as an equation: a rectangle 7 cm long has a perimeter of 30 cm, and perimeter = 2 × (length + width), so 2(x + 7) = 30. Step 3: solve it: x + 7 = 15, x = 8. Step 4: check by putting it back, and give the unit: 2 × (8 + 7) = 30, so the width is 8 cm. The answer may be a decimal or a fraction. Another way is plain arithmetic backwards: 30 ÷ 2 = 15, 15 − 7 = 8; an equation saves thinking backwards — you write it the way the story tells it.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A rectangle is 1 cm longer than it is wide, and its perimeter is 76 cm. How wide is it, in cm?
Show the answer and working
Answer: 18.5 cm
Let the width be x cm, so the length is x + 1: 2(x + x + 1) = 76; 2x + 1 = 38; 2x = 37; x = 18.5.
Example 2
20% of a number is 6. Let the number be x. Which equation is right?
- A. x ÷ 20% = 6
- B. 20% × x = 6
- C. x − 20% = 6
- D. 6 × 20% = x
Choose the right answer
Show the answer and working
Answer: B. 20% × x = 6
“20% of the number” is 20% × x, and it equals 6: 20% × x = 6, x = 30.
Example 3
A square has the same perimeter as a rectangle 17 cm long and 6 cm wide. How long is a side of the square, in cm?
Show the answer and working
Answer: 11.5 cm
Let the side be x cm: 4x = 2 × (17 + 6) = 46; x = 46 ÷ 4 = 11.5.
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