The sum of two number is 49. Twice the larger is eight more than three times the smaller. Find the larger number.

the larger number is 29.4

Step-by-step explanation:

Let x be the larger number

Let y be the second number.

x + y = 49 solve for y

y = 49 - x Substitute this value of y into 2x = 3y + 8

2x = 3y + 8 Second equation

2x = 3 (49 - x) Remove the brackets

2x = 147 - 3x Add 3x to both sides.

2x + 3x = 147 Combine like terms on the left

5x = 147 Divide by 5

5x/5 = 147/5

x = 29.4