A woman spent 1/3 of her money at the market 1/4 at the chemist 1/6 at the electrical shop and had 555 left how many much money did she have to start with
Let's assume the amount of money she had to start with is 'x'.
She spent 1/3 of her money at the market, which is (1/3)*x.
She spent 1/4 of her money at the chemist, which is (1/4)*x.
She spent 1/6 of her money at the electrical shop, which is (1/6)*x.
She had 555 left, so the total amount spent is (1/3)*x + (1/4)*x + (1/6)*x.
Adding the total amount spent to the amount left, we have (1/3)*x + (1/4)*x + (1/6)*x + 555 = x.
Multiplying all terms by the common denominator, which is 12, we get (4/12)*x + (3/12)*x + (2/12)*x + 555 = 12x.
Combining like terms, we have (9/12)*x + 555 = 12x.
Subtracting (9/12)*x from both sides, we have 555 = 12x - (9/12)*x.
Simplifying the equation, we have 555 = (36/12)*x - (9/12)*x.
Combining the terms on the right side, we have 555 = (27/12)*x.
Dividing both sides by (27/12), we have x = 555 * (12/27).
Simplifying the equation, we have x = 740.
Therefore, she had 740 dollars to start with.
To find out how much money the woman had to start with, we can follow these steps:
Step 1: Let's assume the total amount of money she had originally is "x".
Step 2: She spent 1/3 of her money at the market, which is (1/3)x.
Step 3: After the market, she had (x - (1/3)x) = (2/3)x left.
Step 4: She then spent 1/4 of her remaining money at the chemist, which is (1/4)*(2/3)x = (2/12)x = (1/6)x.
Step 5: After the chemist, she had (2/3)x - (1/6)x = (4/6)x - (1/6)x = (3/6)x = (1/2)x left.
Step 6: Lastly, she spent 1/6 of her remaining money at the electrical shop, which is (1/6)*(1/2)x = (1/12)x.
Step 7: After the electrical shop, she had (1/2)x - (1/12)x = (6/12)x - (1/12)x = (5/12)x left.
Step 8: According to the question, she had 555 left, so we can set up an equation: (5/12)x = 555.
Step 9: To solve for x, we multiply both sides of the equation by (12/5): x = 555 * (12/5).
Step 10: Multiplying the values: x = 1665 * 12 / 5 = 3,996.
Therefore, the woman had 3,996 units of currency to start with.
To find out how much money the woman had to start with, we'll need to work backwards. Let's break down the problem step by step:
Step 1: Calculate the amount of money the woman had after spending at the electrical shop.
If she had 555 left after spending at the electrical shop, this means that the amount she spent at the electrical shop is the remaining 5/6 (since 1/6 was spent there).
Let's represent the total amount of money she had after spending at the electrical shop as X:
X - (1/6)X = 555
Simplifying the equation:
(5/6)X = 555
Step 2: Calculate the amount of money the woman had before spending at the electrical shop.
To find the original amount of money she had, we need to divide both sides of the equation by 5/6:
X = 555 / (5/6)
Simplifying further:
X = 555 * (6/5)
X = 666
Therefore, the woman had 666 units of currency to start with.