Question 276977
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:

<pre>
                26.2 * x + 6.8 * y = 1000 (first equation)
                13.6 * x + 6.8 * y =  306 (second equation multiplied by 17)
</pre>
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:


{{{graph(600,600,-100,100,-300,300,(-26.2*x+1000)/6.8,(-.8*x+18)/.4)}}}


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.