Certain items are purchased jointly. If each person pays 8 coins, the surplus is 3 coins, and if each person gives 7 coins, the deficiency is 4 coins. Let x represent the number of people and y the number of coins needed to purchase the items. Find the number of people and the number of coins used to purchase the items.

7 people purchase the items and they used 53 coins

Step-by-step explanation:

Let x represent the number of people.

Let y be the number of coins needed to purchase the items.

If each person pays 8 coins, the surplus is 3 coins. This is illustrated below:

8x = y + 3 (1)

if each person gives 7 coins, the deficiency is 4 coins. This is illustrated below:

7x = y - 4 (2)

Solving by elimination method: subtract equation (2) from equation (1). This is illustrated below:

8x = y + 3 (1)

- (7x = y - 4) (2)

x = 7.

Next, Substituting the value of x into any of the equation to obtain y. In this case I will be using equation 1 as illustrated below:

8x = y + 3 (1)

8 (7) = y + 3

56 = y + 3

Collect like terms

y = 56 - 3

y = 53

Therefore, 7 people purchase the items and they used 53 coins