### sports day lunch set

Question Sample Titled 'sports day lunch set'

On the sports day, the student union is ordering lunch sets for some students. Each student can choose either a hamburger lunch set or a sandwich lunch set. The number of students who choose hamburger lunch set is three times the number of students who choose sandwich lunch set. It is given that the number of the students is ${304}$ . Let ${h}$ be the number of students who choose hamburger lunch set and ${k}$ be the number of students who choose sandwich lunch set.

 (a) Find the values of ${h}$ and ${k}$. (b) The price of hamburger lunch set and sandwich lunch set are $41.8$41.8$ and$48.7$48.7$ respectively. Kathryn estimates that the total price of the lunch for the students is not more than $12800$12800$. Use the method of estimation, or otherwise, explain whether Kathryn is correct or not. (c) In order to make sure the budget is enough, when Liam estimates the total price of the lunch for the students, he firstly rounding up the price of each lunch choice to integer, then multiplies them with corresponding amounts, and finally sums up the parts. Find the percentage error of Liam's estimation.`  (5 marks) 題解  (a) ${h}$ $={304}\times\dfrac{{3}}{{{1}+{3}}}$  $={228}$ 1A ${k}$ $={304}\times\dfrac{{1}}{{{1}+{3}}}$  $={76}$ 1A  (b) Total price $={41.8}\times{228}+{48.7}\times{76}$  $>{41}\times{228}+{48}\times{76}$ 1M  >$12996$>12996$  $\therefore$She is incorrect. 1A  (c) Accurate total price $={41.8}\times{228}+{48.7}\times{76}$  =\$13231.6$=13231.6$ $\therefore$Required % error $=\dfrac{{{42}\times{228}+{49}\times{76}-{13231.6}}}{{13231.6}}\times{100}\%$  $={0.517}\%$ (cor. to 3 sig. fig.) 1A

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