I am finding it difficult to solve the following question, tried solving it by simultaneous equation method but the problem is the value of third equation is unknown.
2 oranges, 3 bananas and 4 apples cost 15.
3 oranges, 2 bananas, and 1 apple costs 10.
What is the cost of 3 oranges, 3 bananas and 3 apples?
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Hint: You don't need to know the cost of a single orange or the cost of a single banana or the cost of a single apple in order to answer the question; you just need to know the cost of $3$ of each. Try adding together the first two equations and considering the ratio of each fruit's price.
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The previous answers found a linear relationship between two equations that produced the third. To solve the problem more generally:
Assume that we form the third purchase by adding $A$ times the first purchase and $B$ times the second purchase. Then, for oranges, bananas and apples respectively: $$2A+3B=3$$ $$3A+2B=3$$ $$4A+B=3$$Note that this set of equations is potentially over-determined; there is not necessarily a solution to the given problem. Solving the first two equations gives:$$A=0.6$$ $$B=0.6$$These values are also (fortunately) a solution to the third equation; the problem has a solution. So, combining the costs of the two purchases in the same way:$$\text{Cost}=0.6\times 15+0.6\times 10=15$$
$\;\;\;\text{ 2 oranges, 3 bananas and 4 apples cost 15.}$
$\underline{ + \;\text{3 oranges, 2 bananas, and 1 apple costs 10.}}$
$=\text{5 oranges + 5 bananas + 5 apples costs }\;25.$
$\Rightarrow \text{1 orange + 1 banana + 1 apple costs}\;5.$
So $\; \text{(3 oranges + 3 bananas + 3 apples) costs }(3 \times 5).$