Jim bought some potted plants:
Petunias cost $11 per pot and Begonias cost $15 per pot.
Jim bought 19 potted plants in all and spent a total of $225 on the plants.
Which would be a correct statement?
Jim bought 15 begonias.
Jim bought 4 petunias.
.
Jim bought 18 begonias.
.
Jim bought 15 petunias
Jim bought 15 petunias.
To find the correct statement, let's set up a system of equations based on the given information:
Let x be the number of petunias bought by Jim.
Let y be the number of begonias bought by Jim.
From the given information, we can form the following equations:
x + y = 19 (Equation 1) (since Jim bought 19 potted plants in total)
11x + 15y = 225 (Equation 2) (since Jim spent a total of $225 on the plants)
To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method here:
Multiply Equation 1 by 11:
11x + 11y = 209 (Equation 3)
Subtract Equation 3 from Equation 2:
(11x + 15y) - (11x + 11y) = 225 - 209
4y = 16
y = 4
Substitute the value of y into Equation 1:
x + 4 = 19
x = 15
Therefore, the correct statement is:
Jim bought 15 petunias.
To determine the correct statement, we can set up a system of equations based on the given information.
Let's represent the number of petunias Jim bought as "p" and the number of begonias as "b."
From the information given, we know the following:
1. Petunias cost $11 per pot, so the total cost of petunias would be 11p dollars.
2. Begonias cost $15 per pot, so the total cost of begonias would be 15b dollars.
3. Jim bought 19 potted plants in total, so the sum of petunias and begonias would be p + b = 19.
4. Jim spent a total of $225 on the plants, so the cost of petunias plus the cost of begonias would be 11p + 15b = 225.
We can now solve this system of equations:
Equation 1: p + b = 19
Equation 2: 11p + 15b = 225
Rearrange Equation 1 to solve for p:
p = 19 - b
Substitute this value of p into Equation 2:
11(19 - b) + 15b = 225
Distribute:
209 - 11b + 15b = 225
Combine like terms:
4b = 16
Divide both sides by 4:
b = 4
Now we have the value for b, which tells us that Jim bought 4 begonias. To find the number of petunias, we can substitute this value back into Equation 1:
p + 4 = 19
p = 15
Therefore, the correct statement is: Jim bought 15 petunias.
y=−2x−1
3x − y =−7
whats a graph to support this
To graph the system of equations y = -2x - 1 and 3x - y = -7, we can plot a few points to represent the lines and then connect them.
For the equation y = -2x - 1, we can choose some arbitrary x-values and calculate the corresponding y-values. Let's choose x = -2, -1, 0, 1, and 2:
For x = -2:
y = -2(-2) - 1 = 3
So one point is (-2, 3).
For x = -1:
y = -2(-1) - 1 = 1
So one point is (-1, 1).
For x = 0:
y = -2(0) - 1 = -1
So one point is (0, -1).
For x = 1:
y = -2(1) - 1 = -3
So one point is (1, -3).
For x = 2:
y = -2(2) - 1 = -5
So one point is (2, -5).
Now let's plot these points on a graph:
For the equation 3x - y = -7, we can rearrange it to solve for y:
-y = -3x - 7
y = 3x + 7
Similarly, we can choose some arbitrary x-values and calculate the corresponding y-values. Let's choose x = -2, -1, 0, 1, and 2:
For x = -2:
y = 3(-2) + 7 = 1
So one point is (-2, 1).
For x = -1:
y = 3(-1) + 7 = 4
So one point is (-1, 4).
For x = 0:
y = 3(0) + 7 = 7
So one point is (0, 7).
For x = 1:
y = 3(1) + 7 = 10
So one point is (1, 10).
For x = 2:
y = 3(2) + 7 = 13
So one point is (2, 13).
Let's plot these points on a graph:
By connecting the plotted points, we can see that the lines intersect at the point (-2, 3).
Therefore, the graph supports the system of equations y = -2x - 1 and 3x - y = -7.