For Those who LOVE math, Help me understand this problem

Test Preparation SAT Preparation
1

<p>I love that title. Anyway In the blue book, test 10 (working backwards) there is this problem on page 953 number 16. It states:</p>

<p>In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5:2. How many pounds of cashews will there be in 4 pounds of this mixture?</p>

<p>Now here is how College Board explains it:</p>

<p>Explanation: The correct answer is 8/7 or 1.14 . Since the ratio of peanuts to cashews is 5:2, it follows that 2/7 of the entire mixture is cashews. 2/7 of a 4-pound mixture is 8/7 pounds. This value can also be expressed as 1.14</p>

<p>What I don't understand if where did CB get the 2/7 from? I'd really appreciate if someone could explain it to me in another way or just clarify more what CB means? Thanks</p>

2

<p>Say you have five pounds of peanuts. That means you have 5 pounds of peanuts and 2 pounds of cashews, right? Your total weight is 7 pounds. Therefore, you have 2/7 is cashews and 5/7 is peanuts. You can multiply those ratios by whatever total weight you’re given. (2/7)* 4 = 8/7. Does that make sense?</p>

3

<p>since the ratio of peanuts to cashews is 5:2, 5/7 will be peanuts and 2/7 will be peanuts. Just multiply (2/7)4 and you get 8/7.</p>

4

<p>WOW quick response :slight_smile: ohhh I completely understand now, Why can’t college board explain it with words and number too. Thank you guys soo much :)</p>

5

<p>Here’s how I solved it:</p>

<p>Let x = the weight of penuts
Let y = the weight of cashews.</p>

<p>So now we can use the problem to give us a system of equations.
x/y=5/7, which implies that 2x=5y
and x+y=4</p>

<p>Now use substitution or your calculator to solve for y (the weight of cashews in a 4 pound mix).</p>

6

<p>Let us assume that we have 5 pounds of peanuts ( or 2 pounds of cashews, you can choose either of the two ).
For every 5 pounds of peanuts , we have 2 pounds of cashews.
OR
For every 2 pounds of cashews , we have 5 pounds of peanuts.</p>

<p>Thus in either case , the total weight of the mixture equals 7 pounds.</p>

<p>By applying unitary method.
For every 7 pounds of the mixture ------> 2 pounds of cashews.
For every 1 pound of mixture ------> 2/7 pounds of cashews.
For every 4 pounds of mixture ------> (2/7)*4 pounds of cashews=1.14 or 8/7 pounds of cashews.</p>