Question
An international food festival charges for admission and for each sample of food. Admission and 3 samples cost $ 5.75. Admission and 6 samples cost $ 8.75. Write a linear function that represents the cost ,y , for any number of samples x?
Hint:
Try to find cost of admission and cost of each sample of food from the given data.
The correct answer is: y = x + 2.75
SOL – No of samples of food = x
Total Cost = y
Let cost of admission = a
Cost of each sample of food = b
Acc. to the question,
Cost of admission and 3 samples = $5.75
a + 3b = 5.75 ---- (1)
Cost of admission and 6 samples = $8.75
a + 6b = 8.75 ---- (2)
Multiply (1) by 2 and subtract (2) from it
2a + 6b = 11.5
- a + 6b = 8.75
_______________
a + 0 = 2.75
Cost of admission, a = 2.75
Substituting value of a in (1)
We get, 2.75 + 3b = 5.75
3b = 3 b = 1
Cost of each sample of food, b = 1
Now, linear function is given by
Total Cost
= no of samples 
cost of each sample + cost of admission
y = x(1) + 2.75
y = x + 2.75
Related Questions to study
Use Substitution to solve each system of equations :
Y = 2X - 4
3X - 2Y = 1
Use Substitution to solve each system of equations :
Y = 2X - 4
3X - 2Y = 1
The graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered. What is the constant rate of change? What does it represent ? What is the initial value ? What might that represent?
The form of a linear equation is y = mx + b in the slope-intercept notation. Variables in the equation are the X and Y. The values m and b represent the line's slope (m) and the value of y when x is 0 and Y is 500. (b). Because the line crosses the y-axis at (0,y), when x is 0, y is referred to as the y-intercept. A two-variable linear equation can be thought of as a linear relationship between y and x or two variables where the value of one (often y) relies on the value of the other (usually x). In this scenario, x is referred to be an independent variable and y as a dependent variable because it depends on the x variable.
Often plotted along the horizontal axis represents the independent variable, x label or not. The majority of linear equations are functions. Alternatively, there is just one value of y for every value of x. You can calculate the value of the dependent variable, y, once the independent variable, x, has been given a value.
The graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered. What is the constant rate of change? What does it represent ? What is the initial value ? What might that represent?
The form of a linear equation is y = mx + b in the slope-intercept notation. Variables in the equation are the X and Y. The values m and b represent the line's slope (m) and the value of y when x is 0 and Y is 500. (b). Because the line crosses the y-axis at (0,y), when x is 0, y is referred to as the y-intercept. A two-variable linear equation can be thought of as a linear relationship between y and x or two variables where the value of one (often y) relies on the value of the other (usually x). In this scenario, x is referred to be an independent variable and y as a dependent variable because it depends on the x variable.
Often plotted along the horizontal axis represents the independent variable, x label or not. The majority of linear equations are functions. Alternatively, there is just one value of y for every value of x. You can calculate the value of the dependent variable, y, once the independent variable, x, has been given a value.
