Problem 32.1 Easy Free

Balancing Fruits

Apples, pears and plums are weighed against each other. One pear plus three apples balance ten plums, and one apple plus six plums balance one pear. How many plums alone would balance one pear?

Work it out, then compare with the answer.

SolutionShow the worked solution

Let $a$ , $p$ and $m$ be the weights of one apple, one pear and one plum. The two balances say

p + 3a = 10m, \qquad p = a + 6m .

Substitute the second equation into the first to eliminate $p$ :

(a + 6m) + 3a = 10m \quad\Longrightarrow\quad 4a = 4m \quad\Longrightarrow\quad a = m .

So an apple weighs the same as a plum. The second balance then gives

p = m + 6m = 7m .

Check: $p + 3a = 7m + 3m = 10m$ , as required.

\boxed{7 \text{ plums}}

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