Question

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The sum of two numbers is 22. Three times one number increased by five is 35. (4 points) a) What are the equations you would use? ¦ and ¦ b) What are the two numbers? and

Answer 1

a) The equations we would use are:

Equation 1: x + y = 22 (sum of two numbers is 22)
Equation 2: 3x + 5 = 35 (three times one number increased by five is 35)

b) To solve the equations, we can use substitution or elimination method.

Using the substitution method:
From Equation 1, we can rearrange it to express x in terms of y:
x = 22 - y

Substituting this value of x into Equation 2:
3(22 - y) + 5 = 35
66 - 3y + 5 = 35
-3y + 71 = 35
-3y = 35 - 71
-3y = -36
y = -36 / -3
y = 12

Substituting this value of y back into Equation 1:
x + 12 = 22
x = 22 - 12
x = 10

So, the two numbers are x = 10 and y = 12.