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Question

Mariam baked some strawberry,apple and pear tarts. There were 12 more strawberry tarts than pear tarts and 20 more apple tarts than strawberry tarts. She sold 3/8 of the apple tarts and half of the strawberry tarts. She had 145 left.
a) How many pear tarts did she bake?
b) How many tarts did she sell together?
Answer for a is 7
Answer for b is 67
Why?
Tks

Answer

Let number of pear tarts = p, strawberry tarts = s, apple tarts = a.

Then s = p+12, a = p+32.

She sold 3/8 of p+32 and she sold 1/2 of p+12, and had 145 tarts left.

So total = 3/8 (p+32) + 1/2 (p+12) +145.

But total also = a + s + p = (p+32) + (p+12) + p.

So 3/8 (p+32) + 1/2 (p+12) + 145 = (p+32) + (p+12) + p.

This gives us 145 = 5/8 (p+32) + 1/2 (p+12) +p = 17/8 (p) + 20 + 6, 145-26 = 17/8 (p).
Therefore p = 119 x 8/17 = 56.
Thus, p =56 and there were 56 pear tarts.

She sold 3/8 of 56+32 apple tarts = 33 apple tarts.
She sold 1/2 of 56+12 strawberry tarts = 34 strawberry tarts.
She sold a total of 67 tarts.

Answers: a) there were 56 pear tarts; b) she sold 67 tarts altogether, out of 212.

Checking: if p = 56, then total tarts = 56 + (56+12) + (56+32) = 212. Yay!

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