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.
How much money did she have to start with?
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.
(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.
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.