Question

The cost of 2 bottles of water and 4 apples is $5.50. The cost of 3 bottles of water and 5 apples is $7.50. Find the cost of one apple and the cost of one bottle of water using elimination. 

Answer 1

You could use a simultaneous equation to work this out. The price of an apple would be 75 cents. The price of a bottle of water would be $1.25.

Answer 2

Answer:

Apple: $0.75

Water bottle: $1.25

Step-by-step explanation:

Let a represent cost of each apple and b represent cost of each water bottle.

We have been given that the cost of 2 bottles of water and 4 apples is $5.50. We can represent this information in an equation as:

$2b+4a=5.50...(1)$

We are also told that the cost of 3 bottles of water and 5 apples is $7.50.We can represent this information in an equation as:

$3b+5a=7.50...(2)$

From equation (1), we will get:

$b=\frac{5.50-4a}{2}$

Upon substituting this value in equation (2), we will get:

$3(\frac{5.50-4a}{2})+5a=7.50$

$\frac{3\cdot 5.50-3\cdot 4a}{2}+\frac{10a}{2}=7.50$

$\frac{16.5-12a+10a}{2}=7.50$

$\frac{16.5-2a}{2}\cdot 2=7.50}\cdot 2$

$16.5-2a=15$

$16.5-16.5-2a=15-16.5$

$-2a=-1.5$

$\frac{-2a}{-2}=\frac{-1.5}{-2}$

$a=0.75$

Therefore, cost of each apple is $0.75.

Upon substituting $a=0.75$ in equation $b=\frac{5.50-4a}{2}$, we will get:

$b=\frac{5.50-4(0.75)}{2}$

$b=\frac{5.50-3}{2}$

$b=\frac{2.50}{2}$

$b=1.25$

Therefore, cost of each bottle of water is $1.25.