Undo discounts before finding fruit prices · source reference

Printed question

Mary runs a fruit stall and keeps a record of the daily sales revenue. The weights of fruits and total amounts received from the sales of three particular types of imported fruits in the past three days are shown in the following table.

Day	Black seedless grapes (kg)	Premium red cherries (kg)	Premium black plums (kg)	Total amount received from sales in dollars
Day 1	17.5	8.1	15.5	580.94
Day 2	12.1	7.5	13.1	431.93
Day 3	18.5	9.6	12.6	602.75

On Day 1, all the fruits were sold at their original prices. On Day 2, Mary gave a special one-day discount of 6% for all purchases. On Day 3, Mary increased the price per kg of premium red cherries by 0.40 dollars due to a price increase by the supplier. Find the price per kg of each fruit on Day 1. [4]

[2020/RI/Promo/1]

Printed working

Let $x,y,z$ be the price per kg of Black seedless grapes, Premium red cherries and Premium black plums on Day 1 respectively, in dollars.

For Day 1, $17.5x+8.1y+15.5z=580.94$ — (1).

For Day 2, $12.1x+7.5y+13.1z=\frac{431.93}{0.94}=459.5$ — (2).

For Day 3, $18.5x+9.6(y+0.4)+12.6z=602.75$.

$\Rightarrow18.5x+9.6y+12.6z=598.91$ — (3).

Using GC, we get $x=16.30,y=18.90,z=9.20$.

Teacher notes

Define the variables.

For day 2, discount of 6% $\Rightarrow$ Price is 0.94 of original price.

For day 3, price per kg, $y$, increases by 0.40 dollars $\Rightarrow y+0.4$.

Printed answer key

16.30 dollars / kg of Black seedless grapes, 18.90 dollars / kg of Premium red cherries, 9.20 dollars / kg of Premium black plums.

Source provenance

2025 TJC H2 Math (9758) JC2 MSM: EQUATIONS. Question sheet printed pages 15–19; solution sheet printed pages 1–12. Original exam attribution is retained above. Currency dollar signs are spelled out outside maths to avoid confusing currency with TeX delimiters.