Three apples and four bananas cost 4.85. Three apples and 10 bananas cost 8.75. Find the cost of the apple

Question

System of equations with word problems 

Answer 1

A = cost of apples

B = cost of bananas

This is your system of equations:

3A + 4B = $4.85

3A + 10B = $8.75

 

There are several ways to solve this. 

 

The first way is using a substitution method:

 

Notice that in both equations, you have the same number of apples. 

Let's isolate the expression for apples in the first equation:

3A = $4.85 - 4B

 

Let's plug in the right hand side of the above equation into the second equation for 3A:

3A + 10B = $8.75 --->  $4.85 - 4B + 10B = $8.75

 

Now, we only have one variable which we can solve for:

$4.85 - 4B + 10B = $8.75

6B = $3.9

B = $0.65 <--cost of bananas

 

We can use this now to solve for A:

3A + 4B = $4.85

3A = $4.85 - 4B

3A = $4.85 - 4(0.65)

3A = $2.25

A = $0.75 <---cost of one apple

 

Double check using either original equation:

3(0.75) + 10(0.65) = 8.75

2.25 + 6.50 = 8.75

8.75 = 8.75 

 

Another way to solve this is using an elimination method where we multiply both equations by some number to eliminate the B variable when we sum the two equations:

 

(3A + 4B = $4.85)*10
(3A + 10B = $8.75)*4

 

30A + 40B = 48.50

12A + 40B = 35.00

 

Subtract the second equation from the first:

18A = 13.50

A = 0.75

 

 

Hope this helps!