stolen from the internet, my mistake was using X for peanuts and Y for almonds but my instinct at first was not to.
Type Cost per pound Pounds Total Cost-- -—————- -—- -———-Peanuts $3.00 12 3(12) = 36Cashews $6.00 x 6xMixture $4.20 12+x 4.20(12+x)
Here are some explanations for why I set the chart up this way. The peanuts line is pretty self-explanatory. The amount for the cashews is the unknown, because you know the least about that part of the problem. The mixture is made up of cashews and peanuts, so the amount of the mixture is the same as the amount of peanuts + the amount of cashews. From here, we know that the cost of the peanuts and cashews must be the same as the mixture: 36 + 6x = 4.20(12+x). Now we must simplify the equation to obtain the amount of cashews needed to satisfy the problem.
36 + 6x = 4.2(12+x)36 + 6x = 50.4 + 4.2x Distributive property6x – 4.2x = 50.4 – 36 Get the variables on one side and theconstants on the other1.8x = 14.4 Combine like termsx = 8 Division property of equality
We now have a value that we anticipate is the answer. Let’s check to see if it makes sense:
12 pounds of peanuts @ $3.00 per pound costs $368 pounds of cashews @ $6.00 per pound costs $4820 pounds of mixture @ $4.20 per pound costs $84
$36 + $48 does equal $84; therefore 8 pounds of cashews does make this situation hold true.
Indeed, our country was nearly overthrown 3 weeks ago, and now we are being told to just “…move on…”