Question

Kevin is having a party and he needs to buy the ingredients to make guacamole. At the first supermarket, he bought 6 limes and 2 avocados for a total of $7.50. Later the same day, he bought 2 more limes and 1 more avocado for a total of $3.00. What was the price of each type of fruit? Let x represent _____________________________ Let y represent _____________________________ System: _____________________

Solution: x = ____________ y = ____________

Answer 1

Let x represent: the price per lime.

Let y represent: the price per avocado.

System: 6*x + 2*y = $7.50

2*x + y =$3.00

Solution: x = $0.75 y = $1.50

Explanation:

Here we have two variables, x and y.

Let's take x = price per lime, and y = price per avocado.

We know that when he bought 6 limes and 2 avocados he paid $7.50, so we can write this as:

6*x + 2*y = $7.50

And we also know that when he bought 2 limes and 1 avocado, he paid $3.00

2*x + 1*y = $3.00

Then we have a system of equations:

6*x + 2*y = $7.50

2*x + y =$3.00

Now we want to solve this system,

The first step is isolating one of the variables in one of the equations, let's isolate y in the second equation:

y = $3.00 - 2*x

Now we can replace this into the other equation:

6*x + 2*($3.00 - 2*x) = $7.50

6*x + $6.00 - 4*x = $7.50

$6.00 + 2*x = $7.50

2*x = $7.50 - $6.00 = $1.50

x = $1.50/2 = $0.75

now we can find the value of y.

y = $3.00 - 2*x = $3.00 - 2*$0.75 = $1.50