Question

The price of 3 citrons and 4 fragrant wood apples is 36 units. The price of 4 citrons and 3 fragrant wood apples is 41 units. Find the price of a citron and the price of afragrant wood apple

Answer 1

Given:

The price of 3 citrons and 4 fragrant wood apples is 36 units.

The price of 4 citrons and 3 fragrant wood apples is 41 units.

To find: The price of citron and the price of fragrant wood apple?

Step-by-step explanation:

Let,

The price of citrons = x

The price of fragrant wood apple = y

We can write an equation as

The price of 3 citrons and 4 fragrant wood apples is 36 units.

`3x+4y=36........(1)`

and

The price of 4 citrons and 3 fragrant wood apples is 41 units.

`4x+3y=41......(2)`

Now, Here we use the elimination method,

So, multiply by 4 in Eq.1 and multiply by 3 in Eq. 2

We get,

`\begin{gathered} 12x+16y=144........(3) \\ \\ 12x+9y=123........(4) \end{gathered}`

Now, subract Eq.4 from Eq.3

`\begin{gathered} (12x+16y)-(12x+9y)=144-123 \\ \\ 12x+16y-12x-9y=21 \\ \\ 7y=21 \\ \\ y=(21)/(7) \\ \\ y=3 \end{gathered}`

Put y = 3 in Eq.1

We get,

`\begin{gathered} 3x+4(3)=36 \\ \\ 3x+12=36 \\ \\ 3x=36-12 \\ \\ 3x=24 \\ \\ x=(24)/(3) \\ \\ x=8 \end{gathered}`

Hence, x = 8 and y = 3

Therefore,

The price of citrons = x = 8 units

The price of fragrant wood apple = y = 3 units

Answer: The price of citrons is 8 units and the price of fragrant wood apple is 3 units.