There is a sale on at a clothes shop. All shorts are reduced by 10% and all jeans are reduced by 20%.
The ratio of the original price of jeans to the original price of shorts is 7:5.
The sale price of the shorts is £18.
What is the sale price of the jeans?
[4 marks]

£22.40

Step-by-step explanation:

shorts: 10% off

jeans: 20% off

before discount:

jeans : shorts = 7:5

after discount:

shorts: £18

original price of shorts: £18/0.9 = £20

original price of jeans: j

j/20 = 7/5

5j = 7 × 20

j = 7 × 4

j = 28

original price of jeans: £28

sale price of jeans: £28 × 0.8 = £22.40

   £22.40

Explanation:

The sale price of the shorts is £18

Let's say x is the original price of the shorts.

If there's a 10% discount, then you pay the remaining 90%

sale price = 90% of x = 0.90x

Set this equal to the 18 pounds and solve for x.

0.90x = 18

x = 18/0.90

x = 20

The shorts originally were £20.

The discount saves you 2 pounds.

Let y be the original price of the jeans before the discount.

The price ratio of jeans to shorts is 7:5. This is before the discount for both items.

So,

(jeans price)/(shorts price) = 7/5

y/20 = 7/5

5y = 20*7

5y = 140

y = 140/5

y = 28

The jeans were originally £28 before the discount.

Now apply the 20% price reduction for the jeans.

20% of 28 = 0.20*28 = 5.60

You save £5.60 and the sale price of the jeans is 28-5.60 = 22.40 pounds.

Or you can use this shortcut

80% of 28 = 0.80*28 = 22.40

This shortcut works because if you save 20%, then you pay the remaining 80%

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b