Mathematics- Word problem solution

A word problem question was posted by @gandhibaba yesterday, so i decided to share my solution on my blog. Solution of the previous COMBINATION exercise will be posted soon

Question:
On Monday, Jim bought three oranges and two mangoes at a nearby store for $25. A few weeks later, JIm went to the same store and bought two oranges with ten mangoes paying $34. Given that the prices remain constant, how much does each item cost?

Solution

Let x represent price of a orange
Let y represent price of a mango

From the first statement,
Jimi bought three oranges( i.e 3x) and two mangoes(i.e 2y) at a nearby store for $25

By writing it mathematically,
3x + 2y = 25 ---------------- eq1

From the second statement,
Jim went to same store and bought two oranges(i.e 2x) with ten mangoes (i.e 10y) paying $34

By writing it mathematically,
2x + 10y= 34 ----------------eq2

Solving eq1 and eq2 simultaneously using elimination method.

Multiply eq1 by 2 6x + 4y =50 -----------eq3
Multiply eq2 by 3 6x + 30y= 102------ eq4

Subtracting eq3 and eq 4
We have,
(6x - 6x) +( 4y - 30y)= 50 - 102
-24y= -52
Divide both side by -24
y= -52/-24 y= 2
Substitute y= 2 in eq1
3x + 2y = 25
3x + 2*2 = 25
3x + 4 = 25
3x= 25 - 4
3x = 21
Divide both side by 3
x = 21/3
x= 7

Recall that x and y are used to represent orange and mango price respectively.

Hence, price of a orange is $7 and price of a mango is 2$

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