Question

A potter wants to make some vases with the clay she has. If she makes 8 similar vases with the clay, she will need another 8 kg of clay. If she makes 5 similar vases with the clay, she will have 4 kg of clay left. How many kilograms of clay does the potter have? Explain how you get the answer.


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Answer 1

SOLUTION

GIVEN

• A potter wants to make some vases with the clay she has.

• If she makes 8 similar vases with the clay, she will need another 8 kg of clay.

• If she makes 5 similar vases with the clay, she will have 4 kg of clay left.

TO DETERMINE

The amount of clay the potter have

EVALUATION

Let the potter have y kg clay and each vases require x kg of clay

So by the first condition

8x = y + 8

$\implies \sf{y = 8x - 8 \: \: \: \: - - - - (1)}$

By the second condition

5x = y - 4

$\implies \sf{y = 5x + 4 \: \: \: \: - - - - (2)}$

From Equation 1 and Equation 2 we get

8x - 8 = 5x + 4

$\implies \sf{ 3x = 12}$

$\implies \sf{ x = 4}$

From Equation 1 we get

y = 32 - 8 = 24

Hence the potter have 24 kg of clay

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