Maths-
General
Easy

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?

hintHint:

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
    rightwards double arrow a + 3b = 5.75            ---- (1)
    Cost of admission and 6 samples = $8.75
    rightwards double arrow 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   rightwards double arrow b = 1
    Cost of each sample of food, b = 1
    Now, linear function is given by
    Total Cost
    = no of samples cross times cost of each sample + cost of admission

    y = x(1) + 2.75

    y = x + 2.75

    Related Questions to study

    General
    Maths-

    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

    Maths-General
    General
    Maths-

    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?

    Maths-General

    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.

    General
    Maths-

    When Using substitution to solve system of equations that have no solution or infinitely many solutions, the variables are the same on both sides , How is the solution determined by the constants in the equations?

    When Using substitution to solve system of equations that have no solution or infinitely many solutions, the variables are the same on both sides , How is the solution determined by the constants in the equations?

    Maths-General
    parallel
    General
    Maths-

    Solve the following by using the method of substitution
    fraction numerator X minus 2 Y over denominator 2 end fraction equals 0
    Y = 0.5X + 3

    Solve the following by using the method of substitution
    fraction numerator X minus 2 Y over denominator 2 end fraction equals 0
    Y = 0.5X + 3

    Maths-General
    General
    Maths-

    Recommendations for safely thawing a frozen turkey are provided on the packaging
    a) What is thaw rate of the turkey in hours per pound for refrigerator thawing ? For cold water thawing ?
    b) Write a linear function in the form y = mx + b to represent the time ,t, in hours , it takes to thaw a turkey in the refrigerator as a function of the weight ,W, in pounds of the turkey.