Kelby has some money. She bought a birthday gift for $11 and spent one-half of the remaining money on clothes. She spent 4/5 on gas and used 1/5 of what was left for entertainment. She saved the $28 she had left.

Question

Kelby has some money. She bought a birthday gift for $11 and spent one-half of the remaining money on clothes. She spent 4/5 on gas and used 1/5 of what was left for entertainment. She saved the $28 she had left.  
How much money did she have to start with?

) · Answer

1. Beginning bal. = $X.
2. Bal. = x - 11.
3. Bal. = 1/2(x-11) = 0.5x-5.5.
4. Bal. = 0.2(0.5x-5.5) = 0.1x - 1.1
5. 0.2(0.1x-1.1) = 0.02x - 0.22.
6. Bal. = 0.8(0.02x-0.22) = 0.016x - 0.176 = 28, 0.016x = 28.176, X = $1,761.

Henry · Answer

Beginning bal. = 1761.

unowen · Answer

Let n be the amount she started with. Then:
(n-11)/2=amount after clothes
1/5((n-11)/2))=(n-11)/10= amount after gas
4/5[(n-11)/10]=4(n-11)/50= amount after entertainment.
4n-44/50=28
n=$361 as the amount she started with.