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
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.
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.
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.
The two variables that can be defined to write an equation for this scenario are:
x = number of minutes for fruit cans
y = number of minutes for vegetable cans
The correct variables to define in order to write an equation that matches this scenario are:
x = number of minutes for fruit cans
y = number of minutes for vegetable cans
In this case, we are interested in calculating the number of minutes required to produce the requested 384 cans of food. The given information tells us the production rates for each assembly line: 24 cans of fruit per minute and 64 cans of vegetables per minute.
Based on this information, we can set up the equation as follows:
24x + 64y = 384
This equation represents the total number of cans produced in terms of the number of minutes each assembly line runs. The left side of the equation represents the total number of cans produced, where 24x represents the fruit cans produced in x minutes and 64y represents the vegetable cans produced in y minutes. The right side of the equation represents the total number of cans needed, which is 384 in this case.
By solving this equation, you can determine the values of x and y, which represent the number of minutes required for fruit and vegetable cans, respectively, to fulfill the order for 384 cans of food.