Question

The price of 11 citrons and 7 fragrant wood apples is 123 units. The price of 7 citrons and 11 fragrant wood apples is 111 units. Find the price of a citron and the price of a wood apple.The price of a citron isunits

Answer 1

if we call the price of citrons c and the price of fragrant wood apples f, then the first statement of the question gives us the equation

`11c+7f=123`

and the second statement gives

`7c+11f=111`

Hence, we have a system of equations with two unknowns and 2 equations which we need to solve in order to answer our question.

Let us solve for c in the first equation. Doing this gives

`c=(123-7f)/(11)`

putting that into the second equation gives

`7((123-7f)/(11))+11f=111`
`(861)/(11)-(49f)/(11)+11f=111`
`(861)/(11)+(72)/(11)f=111`
`\textcolor{#FF7968}{f=5}`

With the value of f in hand, we put it into the first equation and solve for c:

`11c+7*5=123`
`11x+35=123`
`\textcolor{#FF7968}{c=8.}`

Hence, the price of citron is 8 units and the price of the fragrant wood apples is 5 units.