Alex, Michelle and Nurul baked some pineapple tarts. Alex baked twice as many pineapple tarts as Michelle. When Michelle gave 1/3 of her pineapple tarts to Alex and Nurul gave 5/7 of hers to Alex, Alex had a total of 859 pineapple tarts. Nurul had 58 pineapple tarts left in the end. How many pineapple tarts had Michelle left?
To solve this question, let's break it down step by step:
Let's assume the number of pineapple tarts that Michelle baked is x.
According to the given information, Alex baked twice as many pineapple tarts as Michelle, so Alex baked 2x pineapple tarts.
When Michelle gave 1/3 of her pineapple tarts to Alex, she gave away (1/3)x pineapple tarts. Therefore, Michelle had (x - (1/3)x) = (2/3)x pineapple tarts left.
When Nurul gave 5/7 of her pineapple tarts to Alex, she gave away (5/7)(2x) = (10/7)x pineapple tarts. Therefore, Nurul had ((2x) - (10/7)x) = ((4/7)x) pineapple tarts left.
According to the question, Alex had a total of 859 pineapple tarts. So, we can write the equation:
2x + (1/3)x + (10/7)x = 859
To solve the equation, we need to find the value of x.
Multiplying each term in the equation by the least common denominator (LCD) of 3, 7, and 7, which is 21, we get:
42x + 7x + 30x = 21 * 859
Combining like terms, we have:
79x = 18039
Dividing both sides by 79, we get:
x = 18039 / 79 ≈ 228
Therefore, Michelle baked approximately 228 pineapple tarts.
Now, let's find out how many pineapple tarts she had left:
Michelle had (2/3)x = (2/3) * 228 = 152 pineapple tarts left.
So, Michelle had approximately 152 pineapple tarts left.