Question

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13. David begins the summer with a savings of $54.00 more than Fatima. David's job
pays 58.25 per hour. Fatima's job pays $9.75. If they both work the same amount
of time each day, how many hours of work will it take David to have as much
money as Fatima? Write an inequality and then solve.


14. If you use a graph and a table to solve an equation that shows two expressions
equal to one another, how can you use algebra to check your answer?

Answer 1

Answer:

  13.  36 hours

  14.  see below for explanation

Step-by-step explanation:

13. For "w" hours of work, David's assets (in dollars) relative to Fatima's starting value will be ...

  54.00 + 8.25w

Meanwhile, Fatima's assets relative to her starting value will be ...

  9.75w

These values will be equal when ...

  54.00 +8.25w = 9.75w

  54.00 = 1.50w

  54.00/1.50 = w = 36

After David and Fatima both work 36 hours, they will both have the same amount of money.

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14. You check a solution to an equation by substituting the solution value(s) for the variable(s) in the equation and doing the arithmetic. If the equation reduces to a true statement, the solution is correct.

Example:

  f(x) = 2x +5

  g(x) = 3x

A table of ordered pairs for f(x) might be ...

  (x, f(x)) = {(4, 13), (5, 15), (6, 17)}

and a similar table of ordered pairs for g(x) might be ...

  (x, g(x)) = {(4, 12), (5, 15), (6, 18)}

By comparing y-values we can see that f(x) = g(x) = 15 when x = 5. This is our solution found by using a table.

To check the answer, we can put x=5 into the equation ...

  2x +5 = 3x

  2·5 +5 = 3·5 . . . . substitute the value of x for the variable

  10 +5 = 15 . . . . . . simplify a bit

  15 = 15 . . . . . . a true statement; the answer checks OK