Mathematics
OpenStudy (anonymous):

I need help. can someone please help me. Problem solving... Use an inequality and the five-step problem-solving process. I don't know how to do this, can someone show me Jenny, Demi, and Drew by an 18 in. long gourmet sandwich and take it back to their appartment. Since they have different appetites, Jenny cuts the sandwich so that Demi gets half of what Jenny gets and Drew gets three-fourths of what Jenny gets. Find the length of each person's sandwich.

OpenStudy (anonymous):

I don't know why you would use an inequality here. Also the 5 step process is about you learning to plan how to solve a problem, how to reason it out, so I'll say this: The section that Demi and Drew are getting can be described based on Jenny's part. That means you can set up your equation in terms of Jenny only and then solve it. That's your reasoning. Set up your equation based on Jenny's section, then solve and you'll get Jenny's section size. "Demi gets half of what Jenny gets" $Demi=\frac{1}{2}Jenny$ "Drew gets three-fourths of what Jenny gets" $Drew=\frac{3}{4} Jenny$ And, of course, Jenny gets her share. But all added together is 18 inches. So, Demi+Drew+Jenny=18 But we can substitute Demi's and Drew's share as noted above and this becomes: $\frac{1}{2}Jenny+\frac{3}{4} Jenny+Jenny=18$ getting a common denominator: $\frac{2}{4}Jenny+\frac{3}{4} Jenny+\frac{4}{4}Jenny=18$ $\frac{9}{4}Jenny=18$ And so Jenny gets 4*18/9 = 8 inches of sandwich Demi gets half (of 8), that's 4 inches and Drew gets 3/4 (of 8) so that's 6 inches.

OpenStudy (anonymous):

How did you get the common denominator?

OpenStudy (anonymous):

When you have to work with some fractions, the easiest and usually good enough common denominator, is the biggest number on the denominator side. From 2, 4 and 1, In this case, you would choose the 4. Then, can we convert the other fractions to fourths? From 1/2 you ask how would you turn into fourths? The 2 needs to be multiplied times 2 and then you must also do that to the top side. So you get 2/4. The last one doesn't look like a fraction, but it's 1/1 To get the bottom turned into 4 you multiply times 4 and so you do the same on the top, you get 4/4. Hope that's what you were asking.