1.) Megan had a sum of money. She spent $154 on a mobile phone and 2/5 of the remainder on a watch. After that, she had 1/4 of her original sum left. How much money did she have at first?
2.) Leslie bought some sugar. She used 1.8 kg of sugar to bake cookies and 1/6 of the remainder to make cupcakes. She then had 1/3 of the sugar left. Find the mass of sugar she bought.
To solve both of these problems, we will use the concept of working backwards or working in reverse.
1.) Let's find out how much money Megan had at first step by step:
First, we know that Megan spent $154 on a mobile phone.
Let's denote her original sum of money as "x."
After spending $154, she had the remainder, which is (x - $154).
She then spent 2/5 of the remainder on a watch, which means she spent (2/5)*(x - $154) on the watch.
So, the remaining amount after buying the watch is (x - $154) - (2/5)*(x - $154).
According to the given information, Megan had 1/4 of her original sum left after buying the watch. Therefore, this remaining amount is equal to 1/4 of her original sum:
(x - $154) - (2/5)*(x - $154) = (1/4)*x.
Now, we can solve this equation to find the value of x, which represents the original sum of money Megan had.
2.) Similarly, we'll work backwards to find the mass of sugar Leslie bought:
Let's denote the mass of sugar Leslie bought as "y."
First, Leslie used 1.8 kg of sugar to bake cookies.
So, the remainder of sugar is (y - 1.8 kg).
Then, she used 1/6 of the remainder to make cupcakes, which means she used (1/6)*(y - 1.8 kg) of sugar.
Now, the remaining amount of sugar after making cupcakes is (y - 1.8 kg) - (1/6)*(y - 1.8 kg).
According to the given information, Leslie had 1/3 of the sugar left. Therefore, this remaining amount is equal to 1/3 of the original amount of sugar she bought:
(y - 1.8 kg) - (1/6)*(y - 1.8 kg) = (1/3)*y.
Now, we can solve this equation to find the value of y, which represents the mass of sugar Leslie bought.