The gardening store sells clay flower pots, which hold 4 litres of dirt, and ceramic flower pots, which hold 3 litres. Cara bought 27 flower pots, which will hold a total of 94 litres of dirt. How many of each type of flower pot did she buy?
Question
The gardening store sells clay flower pots, which hold 4 litres of dirt, and ceramic flower pots, which hold 3 litres. Cara bought 27 flower pots, which will hold a total of 94 litres of dirt. How many of each type of flower pot did she buy?
Solution
Let's denote the number of clay flower pots as C and the number of ceramic flower pots as F.
From the problem, we have two equations:
-
C + F = 27 (The total number of pots Cara bought is 27)
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4C + 3F = 94 (The total volume of dirt the pots can hold is 94 litres)
We can solve these equations step by step:
Step 1: Multiply the first equation by 3 to make the coefficients of F the same in both equations:
3C + 3F = 81
Step 2: Subtract the new equation from the second equation:
4C + 3F - (3C + 3F) = 94 - 81
This simplifies to:
C = 13
Step 3: Substitute C = 13 into the first equation:
13 + F = 27
Solving for F gives:
F = 27 - 13 = 14
So, Cara bought 13 clay flower pots and 14 ceramic flower pots.
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