There is a spinner with 10 equal areas, numbered 1 through 10. If the spinner is spun one time, what is the probability that the result is a multiple of 5 or a multiple of 2?
The multiples of 5 on the spinner are 5 and 10, and the multiples of 2 are 2, 4, 6, 8, and 10 (which is also a multiple of 5, but we only count it once). Therefore, there are 6 out of 10 possible outcomes that satisfy the condition.
The probability of the result being a multiple of 5 or a multiple of 2 is:
$$\frac{6}{10} = \frac{3}{5} = 0.6$$
So the probability is 0.6, or 60%.
A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 164 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks.
An equation for the total cars and trucks for dealership A:
x + y = 164
An equation for the total cars and trucks for dealership B:
2x + 1/2y = 229
How many cars did dealership A sell?
98
How many trucks did the dealership B sell?
66
To solve for the number of cars sold by dealership A, we can solve for x in the equation x + y = 164. Since we're looking for the number of cars, we can assume that x represents the number of cars sold by dealership A. Then:
x + y = 164
x = 164 - y
To solve for the number of trucks sold by dealership B, we can use the equation 2x + 1/2y = 229 and solve for y, since we're looking for the number of trucks. Then:
2x + 1/2y = 229
1/2y = 229 - 2x
y = 458 - 4x
We know that the total number of cars and trucks sold by dealership A and B adds up to 164 + 229 = 393, so we can set up the equation:
x + y + 2x + 1/2y = 393
Substituting in the expressions for x and y that we found earlier, we get:
(164 - y) + y + 2x + 1/2y = 393
164 + 3/2y + 2x = 393
Substituting in 98 for x (the number of cars sold by dealership A), we get:
164 + 3/2y + 2(98) = 393
164 + 3/2y + 196 = 393
3/2y = 33
y = 22(2/3)
Since we know that y has to be a whole number (representing the number of trucks sold by dealership B), we can round up to 23.
Therefore, dealership A sold 98 cars and dealership B sold 23 trucks.
A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 164 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks
An equation for the total cars and trucks for dealership A:
An equation for the total cars and trucks for dealership B:
How many cars did dealership A sell?
How many trucks did the dealership B sell?
An equation for the total cars and trucks for dealership A:
x + y = 164
(where x is the number of cars sold by dealership A and y is the number of trucks sold by dealership A)
An equation for the total cars and trucks for dealership B:
2x + 1/2y = 229
(where x is the number of cars sold by dealership B and y is the number of trucks sold by dealership B)
To find the number of cars sold by dealership A, we can use the equation:
x + y = 164
We're looking for x, the number of cars sold by dealership A. We can solve for x by subtracting y from both sides:
x = 164 - y
To find the number of trucks sold by dealership B, we can use the equation:
2x + 1/2y = 229
We're looking for y, the number of trucks sold by dealership B. We can solve for y by subtracting 2x from both sides, and multiplying both sides by 2:
y = 458 - 4x
Now we can substitute the expression for x that we found earlier:
y = 458 - 4(164 - y) = 458 - 656 + 4y
Simplifying, we get:
-3y = -198
So y = 66.
Therefore, dealership A sold 164 - 66 = 98 cars, and dealership B sold 66 trucks.
Jim has a total of 77 red and blue marbles. The number of blue marbles is five more than twice the number of red marbles.
Write a pair of linear equations to represent the information. Be sure to state what the variables represent. (2 points)
Explain the substitution method of solving this pair of equations. (2 points)
Solve the equations to find the number of red marbles. Show your work. (3 points)
Let's represent the number of red marbles as "r" and the number of blue marbles as "b".
From the problem, we know that:
r + b = 77 (equation 1)
b = 2r + 5 (equation 2)
The substitution method involves solving one equation for one of the variables, and then substituting that expression into the other equation. This allows us to solve for the other variable.
So let's solve equation 2 for "b":
b = 2r + 5
Now we can substitute this expression for "b" into equation 1:
r + (2r + 5) = 77
Simplifying, we get:
3r + 5 = 77
Subtracting 5 from both sides:
3r = 72
Dividing by 3:
r = 24
Therefore, there are 24 red marbles.
To check our answer, we can substitute r = 24 into one of the original equations:
b = 2r + 5
b = 2(24) + 5
b = 53
And indeed, 24 + 53 = 77, so our answer is correct.
Jim has a total of 77 red and blue marbles. The number of blue marbles is five more than twice the number of red marbles.
Write a pair of linear equations to represent the information. Be sure to state what the variables represent. (2 points)
Explain the substitution method of solving this pair of equations. (2 points)
Solve the equations to find the number of red marbles. Show your work. (3 points)
- Equations: Let r represent the number of red marbles, and b represent the number of blue marbles.
The total number of marbles is 77, so:
r + b = 77
The number of blue marbles is 5 more than twice the number of red marbles, so:
b = 2r + 5
- Substitution method involves solving one equation for one variable, and then plugging that expression into the other equation. By substituting, we can eliminate one variable and then solve for the other. In other words, we find an equation that gives one variable in terms of the other variable and substitute this into the second equation in such a way that only one variable remains.
- Solving for r:
Substitute the expression for b from equation 2 into equation 1:
r + (2r + 5) = 77
Combine like terms:
3r + 5 = 77
Subtract 5 from both sides:
3r = 72
Divide by 3:
r = 24
So, Jim has 24 red marbles. To determine the number of blue marbles, we can substitute r = 24 into equation 2:
b = 2r + 5 = 2(24) + 5 = 53
Therefore, Jim has 24 red marbles and 53 blue marbles.
To find the probability of the spinner landing on a multiple of 5 or a multiple of 2, we first need to determine the total number of favorable outcomes and the total number of possible outcomes.
In this case, the total number of possible outcomes is 10 since there are 10 equal areas on the spinner numbered 1 through 10.
We can find the number of favorable outcomes by identifying the numbers that are multiples of 5 or multiples of 2.
Multiples of 5: 5, 10
Multiples of 2: 2, 4, 6, 8, 10
Since the number 10 appears twice as it is both a multiple of 5 and a multiple of 2, we count it once.
So, there are a total of 6 favorable outcomes.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
Probability = 6 / 10
Simplifying, we get:
Probability = 3 / 5
Therefore, the probability that the result of spinning the spinner is a multiple of 5 or a multiple of 2 is 3/5, which can also be expressed as 0.6 or 60%.