Please help, my mom and I are having a difference of opinion.
The question is crackers come in packages of 24. Cheese slices come in packages of 18. You want one cheese slice for each cracker. What is the least number of crackers and cheese slices you can buy so nothing is left over.
a. 6 crackers and 6 cheese slices
B.48 crackers and 48 cheese slices
c.60 crackers and 60 cheese slices
d. 72 crackers and 72 cheese slices
my mom said see mult up to find a common number so 24x3=72 and 18x4=72
so she said d.
I found that6x4=24 and 6x3=18 so 6 of each, so I said A.
can you please explain who is correct
Thank you
It's 72 crackers and 72 slices of cheese -- not packages.
If you bought 6 packages of crackers and 6 packages of cheese, you'd have 144 crackers and 108 slices of cheese. Well -- that didn't come out even.
Let's look at the least common multiples of 24
24, 48, 72, 96
LCMs of 18
18, 36, 54, 72
Your mom is right. :-)
You need 72 packages of each to come out even.
The total cost is $72.38 (amount Mr. Hernandez spends).
wth
math is answer
Review progress
My husband died lol!!
To solve this problem, we need to find a number that is divisible by both 24 and 18, where the quotient will give us the number of packages needed. Let's break it down step by step.
Your mom's approach:
To find a number divisible by both 24 and 18, your mom multiplied them: 24 x 3 = 72 and 18 x 4 = 72. Since 72 is the same result for both calculations, she believes that the answer is option D (72 crackers and 72 cheese slices).
Your approach:
You multiplied 6 by 4 to get 24 and 6 by 3 to get 18. You concluded that you need 6 of each, so you chose option A (6 crackers and 6 cheese slices).
Explanation of the correct answer:
Your approach is correct. To understand why, we need to find the least common multiple (LCM) of 24 and 18. The LCM is the smallest multiple that is divisible by both numbers.
To find the LCM, we can use prime factorization:
- Prime factorization of 24 = 2^3 x 3^1
- Prime factorization of 18 = 2^1 x 3^2
The LCM is obtained by taking the highest power of each prime factor:
LCM = 2^3 x 3^2 = 24 x 9 = 216
Now, we need to divide the LCM by the number of items in each package to determine how many packages we need to buy:
- Number of crackers per package = 24
- Number of cheese slices per package = 18
Number of cracker packages needed = LCM ÷ 24 = 216 ÷ 24 = 9
Number of cheese slice packages needed = LCM ÷ 18 = 216 ÷ 18 = 12
So, to ensure there's no leftover, you need to buy 9 packages of crackers (9 x 24 = 216 crackers) and 12 packages of cheese slices (12 x 18 = 216 cheese slices).
Neither option A nor option D matches the correct answer, which is 216 crackers and 216 cheese slices.