Undo the discount before finding fruit prices
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. marks
[2020/RI/Promo/1]
Solution
Forming linear systems
Mary records the weights of three imported fruits sold and the total amounts received over three days.
Day 1: 17.5 kg grapes, 8.1 kg cherries, 15.5 kg plums, $580.94. Day 2: 12.1 kg, 7.5 kg, 13.1 kg, $431.93. Day 3: 18.5 kg, 9.6 kg, 12.6 kg, $602.75.
On Day 1 all fruits were sold at original prices. On Day 2 there was a 6% discount on all purchases. On Day 3 the price per kg of cherries was increased by $0.40. Find the price per kg of each fruit on Day 1.
Hint
Let be the Day 1 prices per kg of grapes, cherries and plums.
Day 1 is straightforward. For Day 2, what fraction of the original total was actually paid?
For Day 3, which price changed, and how much extra did that add to the total?
431.93 is the discounted amount. The undiscounted total is , not .
The extra $0.40 per kg applies to cherries only: , not all fruits.
Answer · Q
Grapes 16.30 dollars/kg, cherries 18.90 dollars/kg, plums 9.20 dollars/kg.
Define the unknowns
All three days must be written in terms of the same prices, so we use the original ones.
Day 1
No adjustments: weight times price, summed.
Day 2: undo the 6% discount
A 6% discount means customers paid 94% of the original total. Dividing the amount received by recovers the total at original prices.
Day 3: remove the surcharge
Cherries cost per kg on Day 3, adding to the total. Subtract it to compare with the original prices.
Solve with the calculator
Check in Day 2: ✓.
Explore the idea