IMAT 2013 Q12 [Value]

Coffee granules are available in two jar sizes, regular and large. The regular jar contains 250 grams and costs €4.50. The large jar is 60% bigger, containing 400 grams, but at €6.30 costs only 40% more than the regular jar.

By how much per kilogram is the large jar of coffee better value for money than the regular jar?

A. €3.60
B. €6.00
C. €2.25
D. €3.15
E. €0.90

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.

Approach: find the price per unit of measurement and then compare. In this case, it asked for a better value per kilogram so this is our unit of measurement of choice. Note the percentages they give you in the question could maybe be useful, but it will be faster to solve all of this without their help.

Regular

250g for €4.50

To find the price per kilogram, we can just multiply both by 4.

(250g)(4) = 1000g = 1kg

(€4.50)(4) = €18

So €18/kg

Larger

How can we multiply 400g into 1000g? Multiply by 2.5

(400g)(2.5) = 1000g = 1kg

(€6.30)(2.5) = €15.75

To break this calculation down: (6)(2.5) = 15 and (0.30)(2.5) = 0.30 + 0.30 + 0.15 = 0.75

Final step is to find the difference in unit price between the smaller and larger jar:

€18/kg - €15.75/kg = €2.25

\fcolorbox{red}{grey!30}{Therefore the answer is C, $€2.25$}