Mei Ling brought some money to the school bookshop. She first spent 1/4 of all her money on storybooks. Then she used 2/3 of the remaining money to buy 9 identical highlighters. She had $18 left. How much money did Mei Ling have at first? What was the price of each highlighter?
Try it yourself · watch the animation →Draw the money at first as 4 units. Storybooks take 1 unit, leaving 3 units. How many units are 2/3 of the remainder? How many units is the $18 left?
Answer: Mei Ling at first 72 $; Each highlighter 4 $
Method: Use a bar model to express the fraction of the whole and the fraction of the remainder with the same units. First find how many units the final amount represents, then find the total money at first and the total spent on stationery, and divide by the number of items.
48 $, 4 $ — After spending 1/4 of the whole amount, 3 units are left. Using 2/3 of the remainder on pens means 2 of the 3 units are used, leaving 1 unit. 1 unit = $12, so the money at first = 4 × $12 = $48. The pens cost 2 units = 2 × $12 = $24. Each pen cost $24 ÷ 6 = $4.
90 $, 4.50 $ — Draw the money at first as 4 units. She first spent 1 unit, leaving 3 units. 2/3 of the remainder is 2 units, so 1 unit is left. 1 unit = $22.50, so the money at first = 4 × $22.50 = $90. The folders cost 2 × $22.50 = $45 in total. Each folder cost $45 ÷ 10 = $4.50.
28.80 $, 1.20 $ — The money at first is 4 units. Assessment books cost 1 unit, leaving 3 units. Markers cost 2/3 of the remainder, which is 2 units; 1 unit is left. 12 markers cost 2 units, so 1 marker costs 2/12 unit = 1/6 unit. The amount left was $6 more than the price of 1 marker, so 1 unit − 1/6 unit = 5/6 unit = $6. 1 unit = $6 ÷ 5/6 = $7.20. The money at first = 4 × $7.20 = $28.80. Each marker cost 1/6 unit = $7.20 ÷ 6 = $1.20.
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