Question

Solve each of the following problems using a system of equations. Show all of your work and state your solution in a complete sentence.

1) Tony and Belinda have a combined age of 56. Belinda is 8 more than twice Tony's age. How old is each?

Step 1: Pick a friend or family member to be the character of your word problem. This friend or family member may do one of the following:

Drive a boat
Drive a jet ski

Step 2: Select a current speed of the water in mph.

Step 3: Select the number of hours (be reasonable please) that your friend or family member drove the boat or jets ski against the current speed you chose in step 2.

Step 4:

Select the number of hours that your friend or family member made the same trip with the current (this should be a smaller number, as your friend or family member will be traveling with the current).

Step 5:

Write out the word problem you created and calculate how fast your friend or family member was traveling in still water. Round your answer to the nearest mph.

Follow the 5 steps to complete this problem.

Answer 1

You have 2 unknowns - so 2 variables. You also have enough info to set up 2 diff equations involving both variabls.

Answer 2

Let x = age of belinda and y = age of tony. they have a combined age of 56. Can you make an equation from that?

Answer 3

yes?

Answer 4

what is it?

Answer 5

If my friend and I were 22 and 23 years old, our combined age would be 22 + 23 or 45. The combined age is the SUM of the 2 ages.

Answer 6

belinda is x years old and tony is y years old. Their combined age is 56. Follow the same procedure as I did above to make your equation, but you will have variables instead of numbers.

Answer 7

I should have put 22 + 23 = 45 in my example.

Answer 8

16+40=56

Answer 9

we don't know their ages so we called them x and y, but you have the idea - you want to add them

Answer 10

Solve the following for T and B, Tony's and Belinda's age respectively.\[\{T+B\text{ = }56,B=+8+2T\}\]

Answer 11

So using T and B instead of x and y, we add them to get the combined age of 56:
T + B = 56