Weights

How Much of Each?

1. Which would affect your family more:
   a 2p increase on a loaf of bread, or a 2p increase on the Sunday joint?
2. Why?

Bread and butter go together.

3. Which does your mother buy more of: loaves of bread or pounds of butter?

Milk is used on breakfast cereal and used in other ways.

4. Which does your mother buy more of: packets of cereal or pints of milk?
5. *Write down two more items bought for your family where the same price increase would mean a different increase in weekly payments.

From your answers vou should realise that any shopping list needs to be balanced. You buy some foods more often than others. We can allow for this by finding how much of each item is bought each week.

Tracy's Index
Each week Tracy buys 4 bars of chocolate, 1 portion of fish and chips, and goes to the youth club 3 times.

The numbers 4, 1 and 3 are called WEIGHTS. A 2p increase in the cost of chocolate would affect Tracy 4 times as much as 2p increase in the cost of fish and chips.

1. Make a list of your favourite items from Section A3. For each item decide how often you might pay for it each week. Write down that number beside the item. These numbers are the weights for your spending.

Some of Tracy's calculations are shown in Table 3.

Table 3 - Tracy's spending.

Tracy used the weights to calculate the true increase in cost. She multiplied 4 x 8 (= 32) to find her weekly cost of chocolate last year and 4 x 9 (= 36) to find her weekly cost of chocolate this year.

2. What was Tracy's weekly cost of fish and chips this year?
3. Copy and complete Table 3.
4. Check that Tracy's totals are correct.

Tracy's WEIGHTED INDEX NUMBER for this year:

¹¹⁷/₉₇ x 100 = 121 (to nearest whole number) where last year is the base year.

Your Weighted Pocket Money Index

1. Make out a blank table like Table 3 with the same headings.
2. Write down your items from Section A3.
3. Write down as weights the number of times you pay for each item in a week. Also write in today's prices in the column 'Price this year'.
4. Calculate your weighted index number.
5. Does your answer differ from your unweighted index?
6. Does your weighted index number differ from that of your friend? Why?

Discuss the following questions:

Which of the the index numbers gives you a better idea of how prices affect you?

Why?

Using Individual Index Numbers
John knew that, with last year as base year, the index numbers were:

He used these to help Tracy work out her weighted index number for this year. Table 4 shows some of his working.

John worked out Tracy's weekly cost on chocolate this year, using the index number:

32p x ¹¹³/₁₀₀ = 36p (to nearest penny)

Table 4 - Tracy's costs.

1. Copy and complete Table 4.
2. Find the total weekly cost this year.
3. Hence find the weighted index number for this year.

This shows how individual index numbers can be used to find the weighted index number.

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