Question

Question

The sum of two numbers is 22. Three times one number increased by five is 35.(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a) What are the equations you would use? Response area and Response area

b) What are the two numbers? Response area and Response area

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Answer 1

Let's break down the problem into equations and solve for the two numbers.

a) What are the equations you would use?

1. Sum of the two numbers:
   Let the two numbers be \( x \) and \( y \).
   The first equation is:
   \( x + y = 22 \)

2. Three times one number increased by five is 35:
   The second equation is:
   \( 3x + 5 = 35 \)
   (Assuming \( x \) is the number that is multiplied by three.)

b) What are the two numbers?

Now, let's solve the equations step by step.

1. From the second equation \( 3x + 5 = 35 \):

   • Subtract 5 from both sides:
     \( 3x = 30 \)
   • Divide by 3:
     \( x = 10 \)

2. Now, substitute \( x = 10 \) into the first equation \( x + y = 22 \):

   • \( 10 + y = 22 \)
   • Subtract 10 from both sides:
     \( y = 12 \)

So, the two numbers are:

1. \( x = 10 \)
2. \( y = 12 \)

Final Responses

a) Equations: \( x + y = 22 \) and \( 3x + 5 = 35 \)
b) Numbers: 10 and 12