Question

Angelo bought apples and bananas at the fruit stand. He bought 20 pieces of fruits and spent $11.50. Apples cost $0.50 and bananas cost $0.75. Write a system and solve algebraically to determine how many apples and bananas Angelo bought.

Answer 1

Steps

So for this system, one equation will represent the number of fruit and the other equation will represent the combined total of the fruit. (Let x = apples and y = bananas):

$x+y=20\\0.5x+0.75y=11.50$

Next, I will be using the substitution method to remove one of the variables. To do this, firstly subtract both sides by y in the first equation:

$x=20-y\\0.5x+0.75y=11.50$

Next, since we know that x is equal to 20 - y, substitute it into the second equation and solve for y:

$0.5(20-y)+0.75y=11.50\\10-0.5y+0.75y=11.50\\10+0.25y=11.50\\0.25y=1.50\\y=6$

Now that we have the value of y, substitute it into either equation to solve for x:

$x+6=20\\x=14\\\\0.5x+0.75(6)=11.50\\0.5x+4.5=11.50\\0.5x=7\\x=14$

Answer

In short, Angelo bough 14 apples and 6 bananas.