Question

Nora went into a grocery store and bought 3 apples and 5 mangos, costing a total of $13. Gabriel went into the same grocery store and bought 2 apples and 4 mangos, costing a total of $10. Write a system of equations that could be used to determine the price of each apple and the price of each mango. Define the variables that you use to write the system.

Answer 1

3x + 5y = 13

2x + 4y = 10

x = cost of one apple

y = cost of one mango

Explanation:

To find the equations, you have to multiply the number of apples and mangos by their individual prices and set that equal to the total cost. The prices of each fruit will be represented as variables. You can use any letters for the variables, but in this example, I used x for the price of ONE apple and y for the price of ONE mango.

So: x = apple

y = mango

For the first equation, Nora bought 3 apples for x dollars each. This means the price of those apples is 3 times x, which can be written as 3x because a letter and a number written side by side means they are multiplied. The same applies to the mangos. She bought 5 mangos for y dollars each, which is 5y. The total cost of all of the fruit is $13, so we can set that on one side of the equation as such:

______ = 13

Now we know that all the fruit cost $13, so what represents the total cost of all the fruit? 3x (apples) + 5y (mangos). This is written as 3x + 5y. So we can put this in the blank, leaving us with the equation:

3x + 5y = 13

You repeat the same steps for the second equation. Gabriel bought 2 apples for x dollars each, which becomes 2x. He also bought 4 mangos for y dollars each, which becomes 4y. The total cost of this was $10. So, we can set 2x + 4y (total cost of fruit) equal to $10.

2x + 4y = 10

Your system becomes both equations.

3x + 5y = 13

2x + 4y = 10

x = cost of apple

y = cost of mango

If you need help solving the system, please let me know!