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

Necklace: $85,

Notebook: $8.5

Scarf: $51

Necklace costs $76.5 more than the notebook.

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
`(3)/(5)x`.

The notebook was one-sixth as much as the scarf, so the cost of notebook would be
`(3)/(5)x\cdot (1)/(6)=(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+(3)/(5)x+(1)/(10)x=144.5`

Make a common denominator:

`(10x)/(10)+(3*2)/(5*2)x+(1)/(10)x=144.5`

`(10)/(10)x+(6)/(10)x+(1)/(10)x=144.5`

`(10+6+1)/(10)x=144.5`

`(17)/(10)x=144.5`

`(10)/(17)*(17)/(10)x=(10)/(17)*144.5`

`x=(1445)/(17)`

`x=85`

Therefore, the cost of necklace is $85.

Cost of notebook:
`(1)/(10)x=(1)/(10)*85=8.5`

Therefore, the cost of notebook is $8.5.

Cost of scarf:
`(3)/(5)x=(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.