My Father went shopping with a sum of money. He spent 1/2 of her money plus 50 pesos on a belt. He then spent 1/2 of the remaining money plus 30 pesos on a pair of sandals. Finally he spent 1/5 of what was left plus 20 pesos on a T-shirt . He was left with 15 pesos. How much money did my Father have at first
let Dad start with x
belt: x/2 + 50
amount left = x - (x/2 + 50) = x/2 - 50
sandals: (1/2)(x/2 - 50) + 30 = x/4 + 5
amount left = x/2 - 50 - (x/4 + 5) = x/4 - 55
T-shirt: (1/5)(x/4 - 55) + 20 = x/20 + 9
x/4 - 55 - (x/20 + 9) = 15
x/4 - 55 - x/20 - 9 = 15
x/5 = 79
x = 395 pesos
Try working backwards. We have 15 pesos left. Add 20 and multiply by 5/4,we get 43.75. Add 30, and multiply by 2, we get 147.50. Add 50, and multiply by 2 we get 395 as the amount started with
To solve this problem, we can work backwards. We know that your father was left with 15 pesos after buying the T-shirt. Let's go through the information provided step by step.
Let's assume that the initial amount of money your father had is represented by "x" pesos.
1. After spending 1/2 of his money plus 50 pesos on a belt, your father had (x/2) + 50 pesos remaining.
2. Then, he spent 1/2 of the remaining money plus 30 pesos on a pair of sandals. This means he spent ((x/2) + 50)/2 + 30 pesos, leaving him with ((x/2) + 50)/2 - 30 pesos.
3. Next, he spent 1/5 of what was left plus 20 pesos on a T-shirt. So, he spent (((x/2) + 50)/2 - 30)/5 + 20 pesos, leaving him with (((x/2) + 50)/2 - 30)/5 - 20 pesos, which we know is 15 pesos.
Now, we can set up an equation and solve for x:
(((x/2) + 50)/2 - 30)/5 - 20 = 15
To simplify the equation, let's first get rid of the parentheses:
((x/2) + 50)/2 - 30)/5 - 20 = 15
((x/2) + 50)/2 - 30 = 5 * 15 + 20
((x/2) + 50)/2 = 75 + 20 + 30
((x/2) + 50)/2 = 125
Now, let's solve for x:
((x/2) + 50)/2 = 125
(x/2) + 50 = 2 * 125
(x/2) + 50 = 250
x/2 = 250 - 50
x/2 = 200
To isolate x, we can multiply both sides of the equation by 2:
(x/2) * 2 = 200 * 2
x = 400
Therefore, your father initially had 400 pesos.