A toy company manufactures miniature cars. They sell miniature sports cars in a box. They sell 12 miniature trucks in a box. Mrs. Murphy wants to buy an equal number of sports cars and trucks for the Boys and Girls Club. What is the least number of miniature sports cars she can buy? I need help.
There is too much words.
The least number of miniature sports cars she can buy is 60 cars which is 5 boxes.
LCM(10,12) = 60
All multiples of 10 end in 0
What's the first multiple of 12 that ends in 0? Well, 2*5 = 10, so 5*12 = 60
Or, using the factors,
10 = 2*5
12 = 2^2 * 3^1
The LCM must contain the highest power of each prime divisor
In this case, that's 2^2 * 3 * 5 = 60
Sorry I mean, A toy company manufactures miniature cars. They sell 12 miniature cars in a box. They sell 10 miniature trucks in a box. Mrs. Murphy wants to buy an equal number of sports cars and trucks for the Boys and Girls Club. What is the least number of miniature sports cars she can buy?
I don't know how I messed that up. I really just need for someone to explain the process. My teacher gave us the answer which is 60. Angela is right. But I need someone to explain how my teacher got the answer.
To find the least number of miniature sports cars Mrs. Murphy can buy, we need to determine the least common multiple (LCM) of the quantities of sports cars and trucks sold in a box.
In this case, the company sells miniature sports cars in a box and miniature trucks in a box. We want to find the least number of miniature sports cars Mrs. Murphy can buy such that she can also purchase an equal number of miniature trucks.
Given that the company sells 12 miniature trucks in a box, we need to find the least common multiple between the number of sports cars and 12.
Now, to find the LCM, we can prime factorize the number 12 and the number of sports cars.
The prime factorization of 12 is 2^2 * 3^1, and since we don't know the specific number of sports cars, we'll refer to it as 2^a * 3^b.
To find the LCM, we take the highest power of each prime factor from the two factorizations:
- For 2, we take the highest power min(2^2, 2^a) = 2^max(2, a).
- For 3, we take the highest power min(3^1, 3^b) = 3^max(1, b).
Since we want an equal number of sports cars and trucks, a and b should be the same. So, we have:
2^max(2, a) = 3^max(1, b).
To make it simpler, we can write it as:
2^max(2, a) = 3^m (where m is max(1, b)).
Now, we need to compare the powers of 2 and 3. Since 3 is prime, the only way for 3^m to be equal to a power of 2 is if m = 0.
Therefore, a must be at least 2 to make the equation true. The least number for a is 2.
So, the least number of miniature sports cars Mrs. Murphy can buy is 2.
In summary, Mrs. Murphy needs to buy at least 2 miniature sports cars to have an equal number of sports cars and trucks for the Boys and Girls Club.
It would help if you proofread your questions before you posted them.
How many miniature sports cars are in a box? Angela is assuming there are 12 in a box, which would mean that Mrs. Murphy would only need to buy one box of each.