IMAT 2013 Q19 [Washing Powder]

My packet of washing powder claims to contain enough powder for 24 washes. This claim is based on using the plastic scoop supplied with the packet and filling it once for each wash.

Living in a soft water area I find I only need to fill the scoop three­-quarters full.

How many washes can I get from this packet?

A. 42
B. 18
C. 32
D. 26
E. 30

Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
    • Eliminate any non-essential information
  • Draw a picture, graph, or equation
    • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.

We know that when we use full scoops we have enough powder for 24 washes. If we use 3/4 of a scoop, we can find the new amount of washes by setting 24 = 3x/4. Why do we do this? Because it simplifies this calculation: we will have an extra (24)(1/4) worth of scoops of powder, we can take this answer and divide it by 3/4 to find out how many more of this 3/4 scoop loads we can do.

\frac{3x}{4} =24

3x=(24)(4)

3x = 96

x = 32

\fcolorbox{red}{grey!30}{Therefore the answer is C, $32$.}