the results of a survey of 100 households pointed to shoppers having a preference for house brand products in supermarkets It showed that of 280 households with a combined income of $6000 per month, 71 reported buying house brand products from June to December This is compared to 60 during the preceding 6 months - an increase of x%.

Supermarket, Lo-Cost, Cooking Oil, House brand $5.46 (2qt), Commercial Brand $8.10 (2qt)
Kelly's, Bread, $1.60, House brand $1.6 (1lb), Commercial Brand $1.85(lb)
a) calculate the value of x
b) find the values of y and z
(i) The commercial brand cooking oil cost y% more than house brand one
(ii)The commercial brand bread cost z% more than the house brand one.

To calculate the value of x, we can compare the number of households that bought house brand products during the preceding 6 months with the number of households that bought house brand products from June to December.

Given that 280 households with a combined income of $6000 per month reported buying house brand products from June to December, and 71 households reported buying house brand products during the preceding 6 months, we can calculate the percentage increase as follows:

x = ((number of households in June to December - number of households in preceding 6 months) / number of households in preceding 6 months) * 100

x = ((71 - 60) / 60) * 100
x = (11 / 60) * 100
x = 18.33%

Therefore, the value of x is approximately 18.33%.

Now, let's find the values of y and z:

(i) The commercial brand cooking oil costs y% more than the house brand one.

Given that the house brand cooking oil costs $5.46 (2qt) and the commercial brand cooking oil costs $8.10 (2qt), we can calculate the percentage difference as follows:

y = ((commercial brand cooking oil price - house brand cooking oil price) / house brand cooking oil price) * 100

y = ((8.10 - 5.46) / 5.46) * 100
y = (2.64 / 5.46) * 100
y = 48.36%

Therefore, the commercial brand cooking oil costs approximately 48.36% more than the house brand one.

(ii) The commercial brand bread costs z% more than the house brand one.

Given that the house brand bread costs $1.60 (1lb) and the commercial brand bread costs $1.85 (1lb), we can calculate the percentage difference as follows:

z = ((commercial brand bread price - house brand bread price) / house brand bread price) * 100

z = ((1.85 - 1.60) / 1.60) * 100
z = (0.25 / 1.60) * 100
z = 15.63%

Therefore, the commercial brand bread costs approximately 15.63% more than the house brand one.

To summarize:
a) The value of x is approximately 18.33%.
b) The commercial brand cooking oil costs approximately 48.36% more than the house brand one (value of y), and the commercial brand bread costs approximately 15.63% more than the house brand one (value of z).

a) To calculate the value of x, we need to find the percentage increase in the number of households buying house brand products.

Number of households buying house brand products from June to December = 71
Number of households buying house brand products in the preceding 6 months = 60

Percentage increase = [(71 - 60) / 60] * 100
Percentage increase = (11 / 60) * 100
Percentage increase ≈ 18.33%

Therefore, the value of x is approximately 18.33%.

b)
(i) To calculate the value of y, we need to find the percentage difference between the prices of the commercial brand and the house brand cooking oil.

Commercial brand cooking oil price = $8.10
House brand cooking oil price = $5.46

Percentage difference = [(8.10 - 5.46) / 5.46] * 100
Percentage difference = (2.64 / 5.46) * 100
Percentage difference ≈ 48.36%

Therefore, the value of y is approximately 48.36%.

(ii) To calculate the value of z, we need to find the percentage difference between the prices of the commercial brand and the house brand bread.

Commercial brand bread price = $1.85
House brand bread price = $1.60

Percentage difference = [(1.85 - 1.60) / 1.60] * 100
Percentage difference = (0.25 / 1.60) * 100
Percentage difference ≈ 15.63%

Therefore, the value of z is approximately 15.63%.