Mr Sanderson makes some cookies for a festival day. She gave 1/4 of the cookies to her sister and 1/3 of the remainder to a neighbour. If she had 120 cookies left, how many cookies did she make in the beginning?
Linda spent 1/4 of her money on books, 1/3 on food and 1/5 of the remainder on drinks. If she had 18.50 left over, how much did she have at first?
Can you show the working out with the Cross Method, thanks, it's due tomorrow.
D:
no idea what the Cross Method is, but maybe you can fit these solutions into it.
After giving away 1/4, there were 3/4 left, so
x - x/4 - (1/3)(3x/4) = 120
x - x/4 - x/4 = 120
x/2 = 120
x = 240
Similarly, if Linda started out with $x,
x - x/4 - x/3 - (1/5)(5x/12) = 18.50
x - x/4 - x/3 - x/12 = 18.50
x/3 = 18.50
x = 55.50
To solve both problems using the Cross Method, we need to set up equations based on the given information.
1) Mr. Sanderson's Cookies:
Let's represent the number of cookies Mr. Sanderson made initially as "x".
According to the problem, she gave 1/4 of the cookies to her sister, so she had 3/4 of the cookies remaining.
Then, she gave 1/3 of the remaining cookies to her neighbor, so she had 2/3 of the remaining cookies left.
We're given that Mr. Sanderson had 120 cookies left, so we can set up the equation:
2/3 * 3/4 * x = 120
2) Linda's Money:
Let's represent the amount of money Linda had initially as "x".
According to the problem, she spent 1/4 of her money on books, so she had 3/4 of her money remaining.
Then, she spent 1/3 of the remaining money on food, so she had 2/3 of the remaining money left.
Then, she spent 1/5 of the remaining money on drinks, so she had 4/5 of the remaining money left.
We're given that Linda had 18.50 left over, so we can set up the equation:
4/5 * 2/3 * 3/4 * x = 18.50
To solve these equations using the Cross Method, we can cross-multiply and solve for "x".
1) Mr. Sanderson's Cookies:
Cross-multiplying, we get:
2/3 * 3/4 * x = 120
2/3 * 3x/4 = 120
2x/4 = 120
2x = 4 * 120
2x = 480
x = 480 / 2
x = 240
Therefore, Mr. Sanderson made 240 cookies in the beginning.
2) Linda's Money:
Cross-multiplying, we get:
4/5 * 2/3 * 3/4 * x = 18.50
4/5 * 2/3 * 3x/4 = 18.50
24x/60 = 18.50
24x = 60 * 18.50
x = (60 * 18.50) / 24
x = 37 * 18.50 / 24
x = 37 * 18.50 / 12
x = 568.75 / 12
x = 47.40
Therefore, Linda had 47.40 initially.
Using the Cross Method, we've found that Mr. Sanderson made 240 cookies in the beginning and Linda had 47.40 initially.