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

$c=\frac{123-7f}{11}$

putting that into the second equation gives

$7(\frac{123-7f}{11})+11f=111$$\frac{861}{11}-\frac{49f}{11}+11f=111$$\frac{861}{11}+\frac{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\times5=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.