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? (1 point) Responses Jim bought 15 petunias. Jim bought 4 petunias. Jim bought 18 begonias. Jim bought 15 begonias
The correct statement is "Jim bought 15 petunias."
Let's assume Jim bought x number of petunias and y number of begonias.
According to the given information:
Petunias cost $11 per pot, so the total cost for petunias would be 11x.
Begonias cost $15 per pot, so the total cost for begonias would be 15y.
Jim bought 19 potted plants in total, so we can write the equation: x + y = 19. (equation 1)
Jim spent a total of $225 on the plants, so we can write the equation: 11x + 15y = 225. (equation 2)
To find the values of x and y, let's solve these two equations simultaneously.
Multiplying equation 1 by 11 on both sides, we get:
11x + 11y = 209. (equation 3)
Subtracting equation 3 from equation 2, we get:
(11x + 15y) - (11x + 11y) = 225 - 209
4y = 16
Dividing both sides by 4, we get:
y = 4
Substituting the value of y in equation 1, we get:
x + 4 = 19
x = 15
Therefore, Jim bought 15 petunias and 4 begonias.
The correct statement is:
Jim bought 15 petunias.
To solve this problem, we can use a system of equations. Let's assume that Jim bought x petunias and y begonias.
From the given information, we know that:
1) The cost of each petunia is $11, so the total cost of the petunias is 11x.
2) The cost of each begonia is $15, so the total cost of the begonias is 15y.
3) Jim bought a total of 19 potted plants, so the sum of the petunias and begonias is x + y = 19.
4) Jim spent a total of $225, so the total cost of the plants is 11x + 15y = 225.
Now, we have a system of equations:
x + y = 19 --- (Equation 1)
11x + 15y = 225 --- (Equation 2)
To solve for x and y, we can use a method like substitution or elimination.
Let's solve it using elimination method:
Multiply Equation 1 by 11 to make the coefficients of x in both equations equal:
11x + 11y = 209
Now, subtract Equation 2 from this new equation:
11x + 11y - (11x + 15y) = 209 - 225
11x + 11y - 11x - 15y = -16
-4y = -16
Dividing both sides of the equation by -4:
y = 4
Now, substitute the value of y = 4 back into Equation 1 to find the value of x:
x + 4 = 19
x = 19 - 4
x = 15
Therefore, the correct statement would be:
Jim bought 15 petunias.
r u sre
Apologies for the confusion. Let me double-check my calculations.
Using the system of equations:
x + y = 19
11x + 15y = 225
By multiplying the first equation by -11, we get:
-11x - 11y = -209
Adding this to the second equation:
(11x + 15y) + (-11x - 11y) = 225 + (-209)
4y = 16
Dividing both sides by 4:
y = 4
Substituting this value back into the first equation:
x + 4 = 19
x = 19 - 4
x = 15
So, the correct statement is:
Jim bought 15 petunias.