Answer:
Necklace: $85,
Notebook: $8.5
Scarf: $51
Necklace costs $76.5 more than the notebook.
Step-by-step explanation:
Let x represent cost of the necklace.
We have been given that Elise saved $184. She bought a scarf, a necklace, and a notebook.
The scarf cost three-fifths the cost of the necklace, so the cost of scarf would be
.
The notebook was one-sixth as much as the scarf, so the cost of notebook would be
.
We are also told that she still have $39.50, so the cost of all items would be: ![\$184-\$39.50=\$144.5](https://tex.z-dn.net/?f=%5C%24184-%5C%2439.50%3D%5C%24144.5)
Now, we will equate cost of all items equal to $144.5 as:
![x+\frac{3}{5}x+\frac{1}{10}x=144.5](https://tex.z-dn.net/?f=x%2B%5Cfrac%7B3%7D%7B5%7Dx%2B%5Cfrac%7B1%7D%7B10%7Dx%3D144.5)
Make a common denominator:
![\frac{10x}{10}+\frac{3*2}{5*2}x+\frac{1}{10}x=144.5](https://tex.z-dn.net/?f=%5Cfrac%7B10x%7D%7B10%7D%2B%5Cfrac%7B3%2A2%7D%7B5%2A2%7Dx%2B%5Cfrac%7B1%7D%7B10%7Dx%3D144.5)
![\frac{10}{10}x+\frac{6}{10}x+\frac{1}{10}x=144.5](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B10%7Dx%2B%5Cfrac%7B6%7D%7B10%7Dx%2B%5Cfrac%7B1%7D%7B10%7Dx%3D144.5)
![\frac{10+6+1}{10}x=144.5](https://tex.z-dn.net/?f=%5Cfrac%7B10%2B6%2B1%7D%7B10%7Dx%3D144.5)
![\frac{17}{10}x=144.5](https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B10%7Dx%3D144.5)
![\frac{10}{17}*\frac{17}{10}x=\frac{10}{17}*144.5](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B17%7D%2A%5Cfrac%7B17%7D%7B10%7Dx%3D%5Cfrac%7B10%7D%7B17%7D%2A144.5)
![x=\frac{1445}{17}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1445%7D%7B17%7D)
![x=85](https://tex.z-dn.net/?f=x%3D85)
Therefore, the cost of necklace is $85.
Cost of notebook: ![\frac{1}{10}x=\frac{1}{10}*85=8.5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7Dx%3D%5Cfrac%7B1%7D%7B10%7D%2A85%3D8.5)
Therefore, the cost of notebook is $8.5.
Cost of scarf:
.
Therefore, the cost of scarf is $51.
To find the difference between cost of necklace and notebook, we will subtract $8.5 from $85 as:
![\$85-\$8.5=\$76.5](https://tex.z-dn.net/?f=%5C%2485-%5C%248.5%3D%5C%2476.5)
Therefore, necklace costs $76.5 more than the notebook.