Alliance Cannery has two assembly lines. One produces 24 cans of fruit per minute; the other produces 64 cans of vegetables per minute. Alliance Cannery just received an order for 384 cans of food, which can be made up of a combination of fruit and vegetables. What two variables can you define to write an equation to match this scenario?
x = number of minutes for fruit cans and y = number of minutes for vegetable cans
x = total number of minutes and y = total number of cans
x = number of minutes for fruit and y = total number of cans
x = total number of minutes and y = number of minutes for vegetabl
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es cans
please clarify
The two variables that can be defined to write an equation to match this scenario are:
1) x = number of minutes for fruit cans
2) y = number of minutes for vegetable cans
Using these variables, the equation to find the number of cans of food that can be produced can be written as:
24x + 64y = 384
This equation represents the constraint that the total number of cans of food produced in x minutes on the fruit assembly line and y minutes on the vegetable assembly line must be equal to the order of 384 cans.
1) x = number of minutes for fruit cans
2) y = number of minutes for vegetable cans
Using these variables, the equation to find the number of cans of food that can be produced can be written as:
24x + 64y = 384
This equation represents the constraint that the total number of cans of food produced in x minutes on the fruit assembly line and y minutes on the vegetable assembly line must be equal to the order of 384 cans.
The equation that represents the canned goods order is 24x + 64y = 384.
x = number of minutes for fruit cans
y = number of minutes for vegetable cans
Explain how to calculate the x- and y-intercepts.
x = number of minutes for fruit cans
y = number of minutes for vegetable cans
Explain how to calculate the x- and y-intercepts.
To calculate the x-intercept, we need to set y = 0 in the equation 24x + 64y = 384 and solve for x. This is because the x-intercept is the point where the line crosses the x-axis, which means the value of y is 0.
So, substituting y = 0, we get:
24x + 64(0) = 384
Solving for x, we get:
24x = 384
x = 384/24
x = 16
So, the x-intercept is (16,0), which means that if Alliance Cannery only produces fruit cans, they can produce 384 cans in 16 minutes.
To calculate the y-intercept, we need to set x = 0 in the equation 24x + 64y = 384 and solve for y. This is because the y-intercept is the point where the line crosses the y-axis, which means the value of x is 0.
So, substituting x = 0, we get:
24(0) + 64y = 384
Solving for y, we get:
64y = 384
y = 384/64
y = 6
So, the y-intercept is (0,6), which means that if Alliance Cannery only produces vegetable cans, they can produce 384 cans in 6 minutes.
So, substituting y = 0, we get:
24x + 64(0) = 384
Solving for x, we get:
24x = 384
x = 384/24
x = 16
So, the x-intercept is (16,0), which means that if Alliance Cannery only produces fruit cans, they can produce 384 cans in 16 minutes.
To calculate the y-intercept, we need to set x = 0 in the equation 24x + 64y = 384 and solve for y. This is because the y-intercept is the point where the line crosses the y-axis, which means the value of x is 0.
So, substituting x = 0, we get:
24(0) + 64y = 384
Solving for y, we get:
64y = 384
y = 384/64
y = 6
So, the y-intercept is (0,6), which means that if Alliance Cannery only produces vegetable cans, they can produce 384 cans in 6 minutes.
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