Question

Solve the system of linear equations algebraically to find the cost of one chocolate bar (x) and one lollipop (y)

Answer 1

Let's denote the cost of one chocolate bar as x and the cost of one lollipop as y.

Given the following system of equations:

3x + 2y = 5
2x + 4y = 8

We can solve this system of equations algebraically using the substitution method:

First, let's solve the first equation for x:
3x + 2y = 5
3x = 5 - 2y
x = (5 - 2y) / 3

Now, substitute this expression for x into the second equation:
2[(5 - 2y) / 3] + 4y = 8
(10 - 4y) / 3 + 4y = 8
10 - 4y + 12y = 24
8y = 14
y = 14 / 8
y = 1.75

Now that we have the value of y, we can plug it back into the equation to find x:
x = (5 - 2*1.75) / 3
x = (5 - 3.5) / 3
x = 1.5 / 3
x = 0.5

Therefore, the cost of one chocolate bar is $0.50 and the cost of one lollipop is $1.75.