Question

Elise saved $184. She bought a scarf, a necklace, and a notebook. After her purchases, she still had $39.50. The scarf cost three-fifths the cost of the necklace, and the notebook was one-sixth as much as the scarf. What was the cost of each item? How much more did the necklace cost than the notebook?

Answer 1

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 $\frac{3}{5}x$.

The notebook was one-sixth as much as the scarf, so the cost of notebook would be $\frac{3}{5}x\cdot \frac{1}{6}=\frac{1}{10}x$.

We are also told that she still have $39.50, so the cost of all items would be: $\ 184-\ 39.50=\ 144.5$

Now, we will equate cost of all items equal to $144.5 as:

$x+\frac{3}{5}x+\frac{1}{10}x=144.5$

Make a common denominator:

$\frac{10x}{10}+\frac{3*2}{5*2}x+\frac{1}{10}x=144.5$

$\frac{10}{10}x+\frac{6}{10}x+\frac{1}{10}x=144.5$

$\frac{10+6+1}{10}x=144.5$

$\frac{17}{10}x=144.5$

$\frac{10}{17}*\frac{17}{10}x=\frac{10}{17}*144.5$

$x=\frac{1445}{17}$

$x=85$

Therefore, the cost of necklace is $85.

Cost of notebook: $\frac{1}{10}x=\frac{1}{10}*85=8.5$

Therefore, the cost of notebook is $8.5.

Cost of scarf: $\frac{3}{5}x=\frac{3}{5}(85)=3*17=51$.

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:

$\ 85-\ 8.5=\ 76.5$

Therefore, necklace costs $76.5 more than the notebook.