Question

A hardware store sells 500 nails for £20. a) Find the values of x and y in the ratios below. b) Explain what the values of x and y represent. c) Why might you want to write the ratios in these ways? Number of nails: cost (p) 500 nails: nails 1:x Number of nails: cost (£) £20 y: £1

Answer 1

In the ratio 1:x, x represents the number of nails you can buy for £1. In the ratio y:£1, y represents the cost of a single nail.

Step-by-step explanation:

a) The first ratio is given as 500 nails to £20. To find the value of x in the ratio 1:x, we need to set up the proportion: 500/£20 = 1/x. Cross-multiplying gives us 500x = £20, and dividing both sides by 500 gives us x = 0.04. So, the value of x is 0.04.

For the second ratio, we are given 500 nails to £20. To find the value of y in the ratio y:£1, we need to set up the proportion: 500/£20 = y/£1. Cross-multiplying gives us 500 = £20y, and dividing both sides by £20 gives us y = 25. So, the value of y is 25.

b) In the ratio 1:x, x represents the number of nails you can buy for £1. In this case, you can buy 0.04 nails for £1. In the ratio y:£1, y represents the cost of a single nail. In this case, a single nail costs £25.

c) Writing the ratios in these ways allows us to compare the number of nails to different monetary amounts. The first ratio allows us to determine how many nails we can buy with a certain amount of money, and the second ratio allows us to determine the cost of a single nail.

Answer 2

The values of x and y in the ratios are 25 and 500, respectively. In the ratio 1:x, x represents the cost in pounds for 1 nail. In the ratio y:£1, y represents the number of nails that can be bought for £1.

Step-by-step explanation:

a) To find the values of x and y in the ratios, we can set up proportions using the information given. The first ratio compares the number of nails to the cost in pounds, and the second ratio compares the number of nails to the cost in pounds as well. So, we have:

500 nails : £20 = 1:x

500 nails : £20 = y : £1

By cross-multiplying and solving for x and y, we get x = 500/20 = 25 and y = 500/1 = 500.

b) In the ratio 1:x, the value of x represents the cost in pounds for 1 nail. In the ratio y:£1, the value of y represents the number of nails that can be bought for £1.

c) Writing the ratios in these ways can help compare the cost of nails to the number of nails and vice versa. It allows us to find the cost of a certain number of nails or the number of nails that can be bought for a specific amount of money.