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%

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.