Question 276977: I need help in solving linear system of two equation, The amount of calcium in one bread is 26.2mm and the iron in the bread is0.8mm and amount of calcium in one banana is 6.8 mm and iron is 0.4mm. The qyestion is how can i find out how much of each food item you need in order to reach those value. The recommened value of calicum is 1000 and the iron is 18mm.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1 bread = 26.2mm calcium and .8mm iron.
1 banana = 6.8mm calcium and .4mm iron.
not sure if you got your scale of measurements right. I would have thought mg (milli-grams), not mm (milli-meters).
no matter, we can still solve, but you should check to see that your got the measurement scale right.
let x = the number of breads needed.
let y = the number of bananas needed.
Total calcium needed = 1000 mm.
Total iron needed = 18 mm.
Equation for calcium would be:
26.2 * x + 6.8 * y = 1000
That's because bread has 26.2 mm of calcium and bananas have 6.8 mm of calcium.
Equation for iron would be:
.8 * x + .4 * y = 18 (second equation)
That's because bread has .8 mm of iron and bananas have .4 mm of iron.
Solve these 2 equations simultaneously and you should have your answer.
Multiply the second equation by 17 to get:
26.2 * x + 6.8 * y = 1000 (first equation)
13.6 * x + 6.8 * y = 306 (second equation multiplied by 17)
Subtract second equation from first equation to get:
12.6 * x = 694
Divide both sides of this equation by 12.6 to get x = 55.07936508
Substitute in first equation to get:
26.2*55.07936508 + 6.8*y = 1000
Solve for y to get:
y = -65.15873016
Substitute for x and y in the second equation to get:
.8*55.07936508 + .8*(-65.15873016) = 18
You have a solution, only the solution is negative.
The solution occurs when x = 55.07936508 and y = -65.15873016.
Since the number of bananas (which is y) can't be negative, then you have no solution.
A look at the graph will show you that, if x is positive, there is no common solution except when y is negative.
A quick check by using numbers of x that are positive will show you that this is correct.
You'll get close, but you won't get right on.
Example:
When x = 0, y = 147 in the first equation, and y = 45 in the second equation.
When x = 20, y = 70 in the first equation, and y = 5 in the second equation.
When x = 40, y = -7 in the first equation, and y = -35 in the second equation.
When x = 55, y = -65 in the first equation, and y = -65 in the second equation.
The numbers are such that there is no valid solution to this equation.
The graph of both equations looks like this:
You can see from the graph of the original 2 equations that they will never meet as long as both x and y have to be positive.
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