Question

Sam has a budget of $24 to buy ham and cheese to make sandwiches. If he bought only ham, he could buy 8 lb. If he bought only cheese, he could buy 3 lb. Let x represent the amount of ham and y represent the amount of cheese. Write an equation in standard form to model the different amounts of ham and cheese he can buy.

Answer 1

Given:

(i) Sam has a budget of $24 to buy ham and cheese to make sandwiches.

(ii) In that money he could buy only 8 lb ham or

(iii) He can buy 3 lb cheese.

(iv) x and y represents the amount of ham and cheese respectively.

To find:

(i) An equation in standard form to model the different amounts of ham and cheese he can buy.

Solution:

Given, Sam can buy 8 lb ham from $24.

So, price of 1 lb ham = $(24/8) = $3

Again, x represents the amount of ham.

So, price of x lb ham = $(3*x) = $3x

Again, Sam can buy 3 lb cheese from $24.

So, price of 1 lb cheese = $(24/3) = $8

Again, y represents the amount of cheese.

So, price of y lb cheese = $(8*y) = $8y

Also, total cost of x lb ham and y lb cheese = $ (3x+8y)

This should be equal to his budget of $24.

So, 3x+8y = 24.

The required equation is 3x+8y = 24.