IMAT 2014 Q9 [Jewellery Business]

Past Papers Solutions Archives
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1

Sally owns a small business which produces hand­-crafted jewellery. The materials used to create a necklace cost €1.50 on average. She pays her staff €5.40 an hour. For a standard piece of jewellery she charges 70% more than it costs to produce.

To make a particular Italian-­style glass necklace it takes 30 minutes. How much does she sell this single necklace for?

A. €11.73
B. €2.94
C. €7.14
D. €11.34
E. €5.40

2

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.

First let’s take our givens:

Material cost: €1.50

Staff cost: €5.40 /hour

Time to make necklace: 30 min

Price of necklace: 70% more than production cost

Approach: find the cost per necklace, take 70% of the cost, and add it to the cost per necklace in order to find the selling price. Why? Because we are looking for 170 % of the necklace price since it is the production cost (100%) + 70% extra.

So:

  1. Cost of labour: Staff cost €5.40 /hour but can make a necklace in 30 min, therefore,

(€5.40 /hour)(0.5 hours) = €2.70

  1. Total cost of necklace = labour + materials

Total cost of necklace = $€2.70 + €1.50

Total cost of necklace = €4.20

  1. Find 70% of €4.20

Since this problem expects us to solve it without a calculator, we can use a useful trick where we divide up the number we are working with. We all know that 70% of €1.00 = €0.70. We have €4 here so we can do $(€0.70)(4) = €2.80.

Now all we have to do is the same thing for the cents. 70% of €0.10 = €0.07. We have €0.20 so we can do $(€0.07)(2) = €0.14

Now we can add them together to find 70% of €4.20

€2.80 + €0.14 = €2.94

  1. Find the selling cost of the necklace:

Selling cost = total cost to make necklace + 70% of total cost to make necklace

Selling cost = €4.20 + €2.94

Selling cost = €7.14

\fcolorbox{red}{grey!30}{Therefore the answer is C, $€7.14$}