Question 1182418
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The conditions of the problem make for an easy setup of the problem using two variables for the numbers of kilograms of the two kinds of cheese:<br>
x = kg of pepper cheddar
y = kg of Pennsylvania Jack<br>
x+y=5  the total number of kilograms is 5
18x+8y=55  the total cost of the mixture is $55 (5 kg at $11 per pound)<br>
Given those two equations, the solution from the other tutor uses substitution to solve the problem.<br>
That is a valid method -- but when the two equations are both in Ax+By=C form, I think elimination is much easier.<br>
8x+8y=40  (1st equation, multiplied by 8)
18x+8y=55
10x=15  (difference between the two equations, eliminating y)
x=1.5<br>
ANSWER: x=1.5 pounds of pepper cheddar; the other 3.5 pounds of Pennsylvania Jack<br>
And here is a very quick and easy non-algebraic method for solving this or any other 2-part mixture problem.<br>
Look at the three prices on a number line -- 8, 11, and 18 -- and observe/determine/calculate that 11 is 3/10 of the way from 8 to 18.<br>
That means 3/10 of the mixture is the more expensive cheese.<br>
ANSWER: 3/10 of 5 kg, or 1.5 kg, of the pepper cheddar and the other 3.5 kg of Pennsylvania Jack.<br>