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?
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.
Beginning bal. = 1761.
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.
To find out how much money Kelby had to start with, we need to work our way backwards through the given information.
Let's assume that the initial amount of money Kelby had is represented by X.
Kelby bought a birthday gift for $11, so we subtract $11 from X to get the remaining amount.
Remaining amount = X - $11
Next, Kelby spent one-half of the remaining money on clothes, which means she spent (1/2) * (X - $11) on clothes.
After she bought clothes, she had (X - $11) - (1/2) * (X - $11) money left.
Next, Kelby spent 4/5 on gas, which means she spent (4/5) * [(X - $11) - (1/2) * (X - $11)] on gas.
After spending money on gas, she had [(X - $11) - (1/2) * (X - $11)] - (4/5) * [(X - $11) - (1/2) * (X - $11)] money left.
Finally, she used 1/5 of what was left for entertainment, which means she used (1/5) * {[(X - $11) - (1/2) * (X - $11)] - (4/5) * [(X - $11) - (1/2) * (X - $11)]} for entertainment.
After spending money on entertainment, she had {[(X - $11) - (1/2) * (X - $11)] - (4/5) * [(X - $11) - (1/2) * (X - $11)]} - (1/5) * {[(X - $11) - (1/2) * (X - $11)] - (4/5) * [(X - $11) - (1/2) * (X - $11)]} money left.
Finally, she saved the $28 that she had left. Therefore, we can set up the equation:
{[(X - $11) - (1/2) * (X - $11)] - (4/5) * [(X - $11) - (1/2) * (X - $11)]} - (1/5) * {[(X - $11) - (1/2) * (X - $11)] - (4/5) * [(X - $11) - (1/2) * (X - $11)]} = $28
Now we can solve this equation to find the value of X, which will give us the initial amount of money Kelby had.