Question

5. Two numbers sum to 40. One number is 8 more than the other number. Find the numbers by each method. a. Numerically: Guess and check or reason numerically to find the numbers. b. Algebraically: Call the first number x. Write an expression for the second number, which is 8 more than the first. Write an equation that says these two numbers add to 40. Solve it.

Answer 1

5 Given sum - 40 and one number is more than 8 to other number. 7 Our Cruess is 16,84 16+ 24 = 40 and 16+8=24. 6 let ist number be x. : and number is x+8. sum=40 = x+ (x+8) = 2x+8 = 40 2a = 40-8 2x = 32 x=16 first number a=16] and number at8 =24]

Answer 2

(a) numerically method:-

The sum of two numbers is 40 and one number is 8 more than the other number so the smaller number would be 16 and other number would be 24 because if we add these both 16+24, it gives the sum equal to 40 and the difference between 16 and 24 is 8. So our guessed answer is satisfying the conditions​. Now we can say, the numbers are 16 and 24.

(b) Algebraically method:-

Let's assume the first number = x

So the other number (which is more than first number) = x+8

According to question, the sum of both numbers is 40 . So we can write:

x+(x+8) = 40

2x+8 = 40

2x= 32

x = 16

So first number is 16.

Other number is (x+8) = 16+8 = 24