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The bar graph shows the number of pens, pencils, rulers, and erasers sold by a store in one week, but the labels are missing.
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The store sold more pens than any other item, erasers were least popular, and more pencils were sold than rulers.
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How many rulers did they sell?
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Let’s spend some time looking at this bar graph to understand it.
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If we look at the 𝑦-axis, we can see a scale that goes up in tens.
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And it’s labelled number of items sold.
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This is because the bar graph shows us the number of different items sold by a store in one week.
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There are four items, pens, pencils, rulers, and erasers.
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And these four items are represented by the four bars in our bar graph.
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But unfortunately, if we look at our 𝑥-axis, we can’t see any labels.
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We can just see the general heading, items.
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Now, the question asked us, how many rulers did the store sell?
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But how can we work this out?
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How can we read the graph if we don’t know which of the bars represents rulers?
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Well, in the next part of the problem, we’re given some clues to help us.
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Let’s read through it carefully and try to work out which of the four bars represents rulers.
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The first clue we’re given is that the store sold more pens than any other item.
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Another way of saying this is that pens were the most popular item; they had the most sales.
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We know that the higher up the scale we go on the side of our bar graph, the more sales we can see.
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And so, we’d expect the bar that represents the most sales to be the tallest.
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The third bar’s the tallest, so this must represent the item that sold the most.
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We know these are the pens, so we can label this bar to help us remember what it represents.
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The next clue we’re given is that erasers were least popular.
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In other words, they sold the least amount.
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Which of our bars might represent the least sales?
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We’d expect the bar on our bar graph that shows the lowest sales to be the shortest.
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And we can see straightaway that the final bar on our graph is the shortest.
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It shows the least popular item.
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So, let’s label this bar erasers.
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Remember our question asked us, how many rulers did the store sell?
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So far, we know that the bar that represents rulers isn’t the third or fourth bar.
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It must be one of the first two.
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Let’s look at our final clue.
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We’re told more pencils were sold than rulers.
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We’ve already labelled the pens and erasers, so the pencils and rulers must be the first two bars.
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But which is which?
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If more pencils were sold than rulers, we’d expect the bar that represents pencils to be taller.
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And the taller of these two bars is the first.
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So, this must be the one that represents the number of pencils that were sold.
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This means the only remaining bar must be the one that represents the rulers that were sold.
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And now we can solve the problem.
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How many rulers did the store sell?
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First, we can find the bar that represents rulers, which is the second one.
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And then, we can read across from the top of our bar all the way to the scale on the left-hand side, on the 𝑦-axis.
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We can see that it’s the same height as the number 30.
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We used the clues that we were given to work out which bar represented which item.
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The second bar along represents the number of rulers.
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And so, the number of rulers that the store sold in one week is 30.