Question

The sum of two numbers is 58. The first number is 8 less than half the second number. Let c rep

number. Let d represent the second number. Which statements about solving for the two numbe
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 seco
The equation C=d-8 represents the relationship between the two numbers.
The equation C=d-8 represents the sum of the two numbers.
The number d is 14.
The number c is 44.
The number is 14

Answer 1

The following are the correct choices

First : The equation c + d represents the sum of the two numbers

Third: The equation c = (1/2)d - 8 represents the relationship

and the last choice : The number c is 14

Explanation:

Translate the word problem into equations and solve for c and d where c is the first number and d the second

Sum is 58 translates to

c + d = 58 (1) ===> First choice

First number is 8 less than half the second number translates to

c = (1/2)d - 8 (2) ==> Third choice

Multiply equation (2) by 2 on both sides giving

2c = d - 16 ==> 2c - d = -16 (3)

Add equations (1) and (3) giving

c + d + 2c - d = 58-16

3c = 42

c = 42/3 = 14 ===> Last choice

Substituting for c in equation (1) gives

14 + d = 58

d = 44