Question

Wayne and Winston collect old coins. Winston has 8 fewer coins than Wayne has. If you add 4 times the number of coins Wayne has and 3 times the number of coins Winston has, the sum is 375. This system of linear equations relates the number of coins Wayne has (x) and the number of coins Winston has (y). y = x − 8 4x + 3y = 375 The best method to solve this system of equations is . Wayne has coins, and Winston has coins.

Answer 1

Answers

Part 1: Substitution method

Part2: Wayne has 57 coins

Part 3: Winston has 49 coins

Explanation

The first step is solve find the equations for the information given.

Let x be the number of coins that Wayne has and y be the number of coins Winstone has.

Winston has 8 fewer coins than Wayne has. y = x − 8

If you add 4 times the number of coins Wayne has and 3 times the number of coins Winston has, the sum is 375. 4x + 3y = 375

Part 1

y = x − 8

4x + 3y = 375

This equations can be solved simultaneously by use of substitution method.

Part 1 and part 2

y = x − 8 (i)

4x + 3y = 375 (ii)

Substitute the value of y with (x - 8) in equation (ii).

4x + 3(x - 8) = 375

4x + 3x - 24 = 375

7x = 375 + 24

7x = 399

Divide by 7 both sides of the equation

x = 399/7

= 57

And y = x - 8

y = 57- 8

y = 49

Wayne has 57 coins

Winstone has 49 coins