Philip can paint a room in 9 hours. If Esteban helps Philip, they can paint the room in 3.6 hours. Which equation can be used to determine the time, x, it would take Esteban to paint the room working alone?

 

A. 9t + 3.6t = 1
Incorrect. The rates of work are not part of the equation.

 

B.  1 9 + 1 x = 3.6
Incorrect. This equation has the sum of the rates equal to the time.

  

 

D.  3.6 9 + 3.6 x = 1
Correct! The amount of work performed by each person is combined and equal to one completed job.

A chemist adds a 75% acid solution to 10 milliliters of a solution that is 15% acid. The function that represents the percent of acid in the resulting solution is f(x) = 10(0.15) + x(0.75) 10 + x, x is the amount of 75% solution added. If the chemist’s assistant adds an 80% acid solution to 20 milliliters of a solution that is 18% acid, what function represents the percent of acid in the resulting solution?

 

A. f(x) = 20(0.80) + x(0.18) 20 + x
Incorrect. This equation has the assistant using 20 milliliters of the 80% solution instead of 18% of the solution.

 

B. f(x) =  10(0.18) + x(0.80) 10 + x
Incorrect. This equation has the assistant using 10 milliliters of the 18% solution instead of 20 milliliters.

 

C. f(x) = 20(0.18) + x(0.80) 10 + x
Incorrect. This equation shows 20 milliliters used in the numerator but only 10 milliliters accounted for in the denominator.

 

D. f(x) = 20(0.18) + x(0.80) 20 + x
Correct! The amounts are correctly substituted into the appropriate places in the formula.

Scuba divers are under intense pressure caused by the weight of the water above them. To compensate, divers fill their tanks with air containing less oxygen than the Earth’s atmosphere. The recommended percent p = 660 d + 33 of oxygen in the air a diver breathes is given by p = where d is the depth, in feet. What equation can be used to find the depth at which a diver can swim if he fills his tank with 3% oxygen?

 

A. 0.03 =  660 d + 33
Incorrect. You do not need to convert 3% to a decimal because p is the percentage.

 

B. p =  660 3 + 33
Incorrect. This equation shows a depth of 3 feet, not a percent of oxygen.

 

C. p =  660 0.03 + 33
Incorrect. The 3% oxygen has been converted to a decimal and substituted in for depth.

 

D. 3 =  660 d + 33
Correct! You correctly substituted the percentage in the appropriate places in the formula.

Tom can paint a fence in 10 hours. If Huck helps Tom, they can paint the fence in 4 hours. Which equation can be used to determine the time, x, it would take Huck to paint the fence working alone?

 

A. 10t + 4t = 1
Incorrect. The rates of work are not part of the equation.

 

B. 1 10 + 1 x = 4
Incorrect. This equation has the sum of the rates equal to the time.

 

C. 10 + 4 x = 40
Incorrect. The equation is correct except it determines how long it would take to paint 40 fences of that size.

 

D. 4 10 + 4 x = 1
Correct! The amount of work performed by each person is combined and equal to 1 completed job.