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

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.