Question

Ayden went into a grocery store and bought 2 apples and 6 peaches, costing a total of $7. Daniel went into the same grocery store and bought 10 apples and 3 peaches, costing a total of $8. Write a system of equations that could be used to determine the price of each apple and the price of each peach. Define the variables that you use to write the system.

Answer 1

2 x + 6 y = 7, 10 x + 3 y = 8 is the system of equation.

Here, x = Cost of 1 apple, y = cost of 1 peach in the grocery store

Explanation:

Let the cost of 1 apple in the grocery store = $x

The cost of 1 peach in the store = $y

Ayden bought 2 apples and 6 peaches

Now, The cost of 2 apples = 2 times (cost of 1 apple) = $2x

and The cost of 6 peaches = 6 times (cost of 1 peach) = $6y

Total amount paid by Ayden = $7

⇒ The cost pf 2 apples + Cost pf 6 peaches = $7

or, 2x + 6 y = 7

Similarly:

Daniel bought 10 apples and 3 peaches

Now, The cost of 10 apples = 10 times (cost of 1 apple) = $10x

and The cost of 3 peaches = 3 times (cost of 1 peach) = $3y

Total amount paid by Daniel = $8

⇒ The cost of 10 apples + Cost of 3 peaches = $8

or, 10x + 3 y = 8

So, the given situation can be represented as system of equations :

2x + 6 y = 7

10x + 3 y = 8

Here, x = Cost of 1 apple,

y = cost of 1 peach in the grocery store