Please help!!!
I have a worksheet of problems to do for homework, most of which I don't understand. My teacher hasn't really been answering my questions well. We are supposed to write equations, but if you have another way, that is fine, too. If you know any of the answers, please respond, even if you only know some.
And please walk me through the problem, along with the answer. That is exactly what my teacher didn't do.
1: At a dance party a group of boys and girls exchange dances as follows: one boy dances with 5 girls, a second boy dances with 6 girls, and so on, the last boy dancing with all of the girls. If b represents the number of boys and g the number of girls, then find b in terms of g.
2: The tens digit of a two-digit number exceeds its units digit by 4. The number exceeds twice the number obtained by reversing the digits of the original number by 10. What is the original number? My teacher gave us an equation for this one. I'm not sure if it is right:
10(x+4)x = 2(10x + (x+4))+10
I have NO idea how he got this equation.
3: The number 66 is divided into smaller numbers. One number is 3 more than twice the other number. Find the larger of the two numbers.
4: Find two consecutive odd integers such that 1/3 the smaller plus twice the larger equals 7 more than the sum of the two numbers. My teacher already gave us an equation for this one, too, but please correct me if it isn't right.
1/3x + 2(x+2) = x + (x + 2) +7
My friend got x = 3/7 but I am not sure if this is right, because I did not get that.
Thank you! Your help is VERY much appreciated!!!
I can only figure out number 1. First you want to make a table.
B 1 2 3 4 5 6 7 this is the #
-----------------------
G 5 6 7 8 9 10 11
and so on. Do you know how many kids there are?? Or at least how many girls there are. That might help you figure out the answer.
That's the problem. You see, if it had said how many kids or how many girls there are, that would have helped. I copied the problem word for word, so that's all there is. Maybe my teacher messed up and forgot some info.
Thanks for helping! :)
No problem!! I was happy to. Thanks for helping me!!
if y cube=10 what is the value of y please explain
b=g-4
66= (3+2x) + x (x is the smaller of the 2 numbers) Then solve for x, and do (3+2x) do get the larger number
I'd be happy to help you with your homework problems! Let's go through each problem step by step:
Problem 1:
In this problem, you are given that the first boy dances with 5 girls, the second boy dances with 6 girls, and so on until the last boy dances with all the girls. We want to find out the relationship between the number of boys (b) and the number of girls (g).
To solve this, let's think about the number of girls each boy dances with. The first boy dances with 5 girls, the second with 6, and so on. Notice that the number of girls each boy dances with increases by 1 each time. So, we can form a pattern: 5, 6, 7, 8, ..., g.
Now, let's look at the boys' numbers themselves. The first boy is represented by 1, the second by 2, and so on. We can form another pattern: 1, 2, 3, 4, ..., b.
Since we are trying to find the relationship between b and g, we can see that b and g both start from 1 and have the same increment of 1. Therefore, b = g.
So, the answer to problem 1 is b = g.
Problem 2:
In this problem, you are given a two-digit number with an unknown tens digit (let's call it x) and an unknown units digit. You are also given two pieces of information: the tens digit exceeds the units digit by 4, and the number exceeds twice the number obtained by reversing the digits of the original number by 10.
Let's break down the problem into equations:
1. The tens digit exceeds the units digit by 4: This can be written as x = units digit + 4.
2. The number exceeds twice the number obtained by reversing the digits of the original number by 10: This can be written as 10x + units digit = 2 * (10 * units digit + x) + 10.
Using these two equations, we can solve for the original number.
The equation your teacher provided: 10(x + 4)x = 2(10x + (x + 4)) + 10 is actually the correct equation derived from the given information.
Problem 3:
In this problem, you are given that the number 66 is divided into two smaller numbers. One of the numbers is 3 more than twice the other number. We want to find the larger of the two numbers.
Let's call the two numbers x and y, where x represents the larger number. We can express the information given as:
1. x + y = 66: The sum of the two numbers is 66.
2. x = 2y + 3: One of the numbers (x) is 3 more than twice the other number (y).
Now, we can solve this system of equations. Substitute x = 2y + 3 into the first equation:
(2y + 3) + y = 66
3y + 3 = 66
3y = 66 - 3
3y = 63
y = 63/3
y = 21
Now, substitute the value of y back into x = 2y + 3:
x = 2(21) + 3
x = 42 + 3
x = 45
So, the larger of the two numbers is x = 45.
Problem 4:
In this problem, you are asked to find two consecutive odd integers. You are given that 1/3 of the smaller integer plus twice the larger integer equals 7 more than the sum of the two numbers.
Let's call the smaller odd integer x. Since the two numbers are consecutive odd integers, the larger integer can be represented as x + 2.
The equation your teacher provided: 1/3x + 2(x + 2) = x + (x + 2) + 7 is actually the correct equation derived from the given information.
Now, let's solve this equation:
1/3x + 2x + 4 = 2x + 2 + 7
1/3x + 2x + 4 = 2x + 9
Combining like terms:
1/3x + 2x - 2x = 9 - 4
7/3x = 5
Multiply both sides by 3/7:
x = (5 * 3)/7
x = 15/7
So, the solution is x = 15/7, which confirms that your friend's answer of x = 3/7 is incorrect.
I hope this explanation helps you understand these problems better. If you have any further questions, feel free to ask!