Application problem

Question

Kathy spent 3 fifths of her money on a necklace and 2 thirds of the remainder on a bracelet. If the bracelet cost $17, how much money did she have at first?

Answer 1

M = money she had at first = $63.75

(2/3)(M-3/5M) = 17 She spent (2/3) of what was left, M-(3/5)M on a bracelet = $17

2M/3 - 6M/15 = 17

10M/15 - 6M/15 = 17

4M/15 = 17

4M = 15(17) = 255

M = 255/4 = $63.75

She had $63.75 originally. She spent 3/5 of it on a necklace or 3/5 x 63.75 = $38.25 leaving her with 63.75-38.25 = $25.50 she spends 2/3 of it on a bracelet, costing $17. 2/3 times $25.50 = $17

she's left with $25,50 - $17 = $8.50

Answer 2

Let her money be y

Money spent on necklace is 3/5 x y = 3y/5

Remainder will be= y/1 - 3y/5 = 5y-3y/5 = 2y/5

Money spent on bracelet = 2/3 of remainder = 2/3 × 2y/5 = $17

4y/15 = $17

Cross multiply

4y = $255

y = $255/4

y = $63.75

Therefore, she had $63.75 at first