<p>In a mixture of peanuts and cashews the ratio by weight of peanuts to cashews is 5 to 2. How many pounds of cashews will there be in 4 pounds of this mixture. </p>
<p>Thank you in advance. I'm just not sure how to approach this problem even though I feel like there is a simple solution. I looked at the CB explanation and it confused me so I would really appreciate the help.</p>
<p>I did it a bit awkwardly, but see if you like it:</p>
<p>A ratio of 5:2 is 5x:2x. Of course, the total is 7x. What we need to find is when the total is equal to 4. 7x = 4. x = 4/7. Well, now we can just plug this 4/7 into the ratio 5x:2x (or just 2x, since that’s the cashews) and find our answer to be 2*4/7, or 8/7.</p>
<p>Thank you 
That helps a lot.</p>
<p>You can also just set up a simple ratio. I like to write down 2 key words for the 2 things being compared. For example here we can use “cashews” and “total” </p>
<p>cashews 2 x
total 7 4</p>
<p>Now just add division symbols and equal signs, then cross multiply and divide.</p>
<p>2/7=x/4
8=7x
x=8/7</p>
<p>Create a ratio / real number chart.</p>
<p>So, I like to set it up like this:</p>
<p>Peanuts : Cashews : Total
5 : 2 : 7</p>
<p>? : ? : 4</p>
<p>To figure this out, you find the “k” or the constant that relates your total to 4. So, 7 * x = 4, so x = 4/7</p>
<p>Now, you divide every by 4/7.</p>
<p>5 * 4/7 = 20/7 (Peanutes) | 2 * 4/7 = 8/7 (cashews)</p>
<p>To verify, you can add them, so 20/7 + 8/7 = 28/7 = 4</p>
<p>So, there are 8/7 pounds of cashews in your bag of nuts. </p>
<p>Hope that makes sense. it’s easier to explain the a whiteboard and a marker :)</p>
<p>LadyBloo, everything the previous posters said is correct, but let me try to explain the concept behind a ratio a little so that it will hopefully help you with other problems. Forgive me it all sounds very elementary. Most students learned all these things in 5th grade but their teachers never bothered to explain that they were all the same thing.</p>
<p>A ratio is any comparison between two amounts, kind of like a recipe.
A fraction is a ratio of part to whole.
A percent is a fraction of 100.</p>
<p>So any ratio problem can be expressed as both a fraction and as a percent.</p>
<p>In your problem, 5/7 of the mixture is peanuts and 2/7 is cashews.</p>
<p>Because this problem doesn’t have an easy common denominator like some do, I would very use a percent ratio by converting the fraction of cashews (2/7) into a percent decimal with my calc and multiply by 4 -> 2 (divided)7 (enter) (times) 4.</p>
<p>Whatever the percent of cashews is in your “recipe” (ratio), will be the percent in ANY amount. </p>
<p>This way of thinking will always work with ratios. Like any SAT question. The real “trick” is understanding the concept behind it.</p>
<p>Sometimes they don’t ask how much of one part of your ratio will be in a certain amount. Instead, they will ask “which of the following could be the amount of peanuts.” Then they’d give you something like, 2, 6, 11, 15, 21. </p>
<p>In this case, the percent idea won’t be nearly as helpful as thinking about it as a fraction. If 5/7 are peanuts, and all the choices are integers, the amount of peanuts must be a multiple of 5. The answer of course, is 15. Just for kicks, what would the total amount of the mixture be if there are 15 pounds of peanuts? Mulitply the denominator by the same thing (5 x THREE = 15) to keep equivalent fractions and you’ll get 3 x 7 = 21.</p>
<p>Like all SAT questions, they are all different yet essentially the same. Knowing HOW to solve it is one thing; understanding why allows you to solve any of them.</p>
<p>I realize this explanation goes beyond what you asked, but I know many students read but don’t post, so hopefully it helped someone.</p>