Back to Math Problems (Ages 14 to 15)
Emily, the owner of a garden center, purchased two types of gardening kits: basic and deluxe. She sold the basic kits at a profit of 30% and the deluxe kits at a profit of 45%. The total profit on the sale of all kits was 40%, and the total selling price for all kits was $16,800.
What did Emily originally pay for each type of gardening kit?
Let’s solve this step by step:
1) Let a represent the cost of basic kits and b represent the cost of deluxe kits.
2) For basic kits: Selling price = 1.30a (30% profit)
For deluxe kits: Selling price = 1.45b (45% profit)
3) Total selling price equation:
1.30a + 1.45b = 16,800
4) Total profit is 40%, so:
1.40(a + b) = 16,800
a + b = 16,800 / 1.40 = 12,000
5) Substituting a = 12,000 – b into the total selling price equation:
1.30(12,000 – b) + 1.45b = 16,800
15,600 – 1.30b + 1.45b = 16,800
15,600 + 0.15b = 16,800
0.15b = 1,200
b = 8,000
6) If b = 8,000, then a = 12,000 – 8,000 = 4,000
Therefore, Emily originally paid $4,000 for the basic kits and $8,000 for the deluxe kits.
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