Kristin bought two sunflower plants. Plant A is 8 inches tall and is growing at a rate of 3 inches per week. Plant B is 12 inches tall and is growing at a rate of 2 inches per week. Write the two equations to represent each sunflower plant if the plants to continue to grow at the same rate. In your equations, x
represents the number of weeks, and y
represents the height of the plant in inches. (1 point)
Plant A: y=
Plant B: y=
Question 2
When will the plants be exactly the same height?
This question requires you to show your work.
(1 point)
The plants will be exactly the same height during week
Plant A: y = 8 + 3x
Plant B: y = 12 + 2x
To find when the plants will be exactly the same height, we can set the two equations equal to each other:
8 + 3x = 12 + 2x
Subtract 2x from both sides:
8 + x = 12
Subtract 8 from both sides:
x = 4
Therefore, the plants will be exactly the same height during week 4.
can you show me how you got that answer
Sure! To find when the plants will be exactly the same height, we set the heights of the two plants equal to each other:
Plant A: y = 8 + 3x
Plant B: y = 12 + 2x
We then set the two equations equal to each other:
8 + 3x = 12 + 2x
To isolate x, we can subtract 2x from both sides:
8 + x = 12
Next, we subtract 8 from both sides:
x = 4
Therefore, the plants will be exactly the same height during week 4.
The Walker and Baldwin families ordered lunch at the refreshment stand at the basketball game. The Walker family ordered 4 hot dogs and 3 cheeseburgers and paid $23.75. The Baldwin family ordered 6 hots dogs and 2 cheeseburgers and paid $25. Write a system of equations using h
for hot dogs and c
for cheeseburgers.(1 point)
Responses
4h − 3c = 23.75
and 6h − 2c = 25
4h − 3c = 23.75
and 6h − 2c = 25
4h + 3c = 23.75
and 6h + 2c = 25
4h + 3c = 23.75
and 6h + 2c = 25
7c = 23.75
and 8h = 25
7c = 23.75
and 8h = 25
h + c = 23.75
and h + c = 25
h + c = 23.75
and h + c = 25
Question 2
What are the prices of a hot dog and a cheeseburger?
This question requires you to show your work.
(2 points)
$4.25 $2.00 $5.00 $2.75
hot dog
cheeseburger
The correct system of equations is:
4h - 3c = 23.75
6h - 2c = 25
To find the prices of a hot dog and a cheeseburger, we can solve the system of equations using the substitution method:
From the first equation:
4h - 3c = 23.75
3c = 4h - 23.75
c = (4/3)h - 23.75/3
Substitute c into the second equation:
6h - 2((4/3)h - 23.75/3) = 25
6h - (8/3)h + 15.83 ≈ 25
(18/3)h - (8/3)h = 25 - 15.83
(10/3)h = 9.17
h ≈ 2.75
Now, substitute h back into the first equation to find c:
4(2.75) - 3c = 23.75
11 - 3c = 23.75
-3c = 12.75
c ≈ 4.25
Therefore, the price of a hot dog is approximately $2.75 and the price of a cheeseburger is approximately $4.25.