Melons cost QR1.5 each and apples cost QR3.75 per kilogram. A man buys apples and melons at the supermarket. Write a formula to describe the total cost of his purchase.
Investigate how many melons and how many kilograms of apples he could buy for QR30.
**QR is a currency :)
First you must define your variables.
In full sentence form define
apples ---> a
melons ---> m
then Cost = 3.75a + 1.5m
second equation:
3.75a + 1.5m ≤ 30
multiply this equation by 4
15a + 6m ≤ 120 , dividing by 3
5a + 2m ≤ 40
2m ≤ 40 - 5a
For m to be a whole number, the right side of the above statement has to be even, so a must be an even number
0 ≤ a ≤ 8
so give a values of 0, 2, 4, 6, and 8
To find the total cost of his purchase, we need to calculate the cost of melons and the cost of apples separately and then sum them up.
Let's denote the number of melons as M and the number of kilograms of apples as A.
The total cost of melons will be the cost of each melon multiplied by the number of melons:
Cost of melons = QR1.5 x M
The total cost of apples will be the cost per kilogram of apples multiplied by the number of kilograms of apples:
Cost of apples = QR3.75 x A
The formula to describe the total cost of the purchase is:
Total cost = Cost of melons + Cost of apples
Now, let's investigate how many melons and how many kilograms of apples he could buy for QR30.
For simplicity, let's assume the man spends all his money on melons and apples.
Using the formula, we can set up the equation:
Total cost = QR1.5 x M + QR3.75 x A
Since the total cost is QR30, we can substitute it into the equation:
QR30 = QR1.5 x M + QR3.75 x A
Now, we need to solve this equation for M and A.
To solve for two variables, we need another equation. However, the problem does not provide one. Therefore, we need to make some assumptions.
Let's assume that the man wants to buy an equal number of melons and kilograms of apples. In this case, the number of melons and the number of kilograms of apples will be the same (M = A).
Using this assumption, we can substitute M for A in the equation:
QR30 = QR1.5 x M + QR3.75 x M
Simplifying the equation:
QR30 = QR5.25 x M
To solve for M, we can rearrange the equation:
M = QR30 / QR5.25
Calculating M:
M = QR5.71
Therefore, the man could buy approximately 5.71 melons and 5.71 kilograms of apples for QR30.