Question

The sum of two numbers is 58. The first number is 8 less than half the second number. Let c represent the first number. Let d represent the second number. Which statements about solving for the two numbers are true? Check all that apply. The equation c + d = 58 represents the sum of the two numbers. The equation c + d = 58 represents the sentence “The first number is 8 less than half the second number.” The equation c = one-half d minus 8 represents the relationship between the two numbers. The equation c = one-half d minus 8 represents the sum of the two numbers. The number d is 14. The number c is 44. The number c is 14. The number d is 44.

Answer 1

Answer: A ,C,G and H are correct statements. Look into the step by step for more understanding.

Step-by-step explanation:

To solve for this problem let's find the actually numbers.

so we know that c + d=58  and also c= 1/2d-8  

We have two systems of equations

c+d = 58

c= 1/2d - 8  

Solve for c   by substitution.  Substitute the second equation into the first one.

1/2d -8 + d = 58   Add 8 to both sides

1/2 +d = 66

3/2d =66     Divide both sides by 3/2

d=44  Now we  know the d which is the second number is 44  so subtract it from 58 to find the first number.

58 - 44 = 14  

we will represent the statements by letters from A going.

A. The equation c + d = 58 represents the sum of the two numbers

B. The equation c+d=58 represents the sentence "The first number is 8 less than half the second number."

C.The equation c= 1/2d -8 represents the relationship between the two numbers.

D. The equation  c= 1/2d - 8 represents the sum of the two numbers.

E. The number d is 14.

F. The number c  is 44.

G. The number c is 14.

H. The number  d is 44.  

Now looking at the statements, A ,C,G and H are all correct.