Hi, there--
.
The Problem:
If 530 pesos can buy 4 kg of fish and 2 kg of pork while 875 pesos can buy 7 kg of fish and 3 kg of
pork, how much does a kg of fish cost?
A Solution:
Let f be the cost of a kg of fish (in pesos)
Let p be the cost of a kg of pork (in pesos)
We need to write two equations using the information in the problem.
530 pesos can buy 4 kg of fish and 2 kg of pork.
The cost of 4 kg of fish is 4 times the cost per kg, or 4f.
The cost of 2 kg of pork is 2 times the cost per kg, or 2p.
[the cost for 4 kg fish] + [cost for 2 kg pork] = [530 pesos]
In algebra, we express this relationship as
4f + 2p = 530
.
875 pesos can buy 7 kg of fish and 3 kg of pork.
Using similar reasoning, we can write a second equation.
7f + 3p = 875.
We now have a system of two equations. We will use the elimination method to solve the system.
Multiply every term in the first equation by 3, and every term in the second equation by -2.
4f + 2p = 530 --------------> 12f + 6p = 1590
7f + 3p = 875 --------------> -14f + -6p = -1750
Add the two equations together. Notice that 6p+ -6p is 0, so the p terms are eliminated.
-2f = -160
Divide both sides of the equation by -2.
f = -160/-2
f = 80
A kg of fish costs 80 pesos. We can find the cost of a kg of pork by substituting 80 for f in either
equation. I'll use the first one.
4f + 2p = 530
4(80) + 2p = 530
320 + 2p = 530
2p = 530 - 320
2p = 210
p = 105
A kg of pork costs 105 pesos.
Check your work by substituting 80 for f and 105 for p in the two original equation.
(I'll leave that for you to do.)
Feel free to email if you have questions about this solution
Ms.Figgy
math.in.the.vortex@gmail.com
