Home
Class 10
MATHS
A delicatessen charges for a certain typ...

A delicatessen charges for a certain type of sald at a rate of 2 dollars for the first half and 75 cents for each additional half pound. Which of the following expressions represents the total charge, in cents, for p pounds of the salad, where p is a positive integer ?

A

`25(6p+8)`

B

`25(6p+5)`

C

`25(3p+5)`

D

`1.25+1.5p`

Text Solution

AI Generated Solution

The correct Answer is:
To find the total charge in cents for p pounds of salad, we can break down the problem step by step: ### Step 1: Understand the pricing structure The delicatessen charges: - $2 for the first half pound - $0.75 (75 cents) for each additional half pound ### Step 2: Convert dollars to cents Since we need the total charge in cents: - $2 = 200 cents - $0.75 = 75 cents ### Step 3: Determine the number of half pounds in p pounds Since 1 pound equals 2 half pounds, p pounds will be: - \( 2p \) half pounds ### Step 4: Calculate the charge for the first half pound The charge for the first half pound is: - 200 cents ### Step 5: Calculate the number of additional half pounds After the first half pound, the number of additional half pounds is: - \( 2p - 1 \) (because we have already accounted for the first half pound) ### Step 6: Calculate the charge for the additional half pounds The charge for the additional half pounds is: - \( 75 \times (2p - 1) \) cents ### Step 7: Combine the charges Now, we can combine the charges: - Total charge = Charge for the first half pound + Charge for additional half pounds - Total charge = \( 200 + 75 \times (2p - 1) \) ### Step 8: Simplify the expression Now, let's simplify the expression: 1. Distribute the 75: \[ 200 + 75 \times 2p - 75 \] This simplifies to: \[ 200 - 75 + 150p = 125 + 150p \] ### Step 9: Final expression Thus, the total charge in cents for p pounds of salad is: \[ 125 + 150p \] ### Final Answer The expression that represents the total charge, in cents, for p pounds of the salad is: \[ 125 + 150p \]
To find the total charge in cents for p pounds of salad, we can break down the problem step by step: ### Step 1: Understand the pricing structure The delicatessen charges: - $2 for the first half pound - $0.75 (75 cents) for each additional half pound ### Step 2: Convert dollars to cents ...
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS TOPICS

    KAPLAN|Exercise MISCELLANEOUS TOPICS FOLLOW - UP TEST|12 Videos

  • MATH TEST-01

    KAPLAN|Exercise Multiple Choice Question|20 Videos

  • PLANE GEOMETRY

    KAPLAN|Exercise PLANE GEOMETRY FOLLOW - UP TEST|6 Videos

Similar Questions

Explore conceptually related problems

Gina subscribes to a cell phone service that charges a monthly fee of $60.00 . The first 500 megabytes of data is free, and the cost is $0.15 for each additional megabyte of data used that month. Which of the following functions gives the cost, in dollars, for a month in which Gina uses x megabytes of data, where x gt 500 .

The chart below shows the number of small and large packages of a certain brand of cereal that were bought over a three - day period. The proce of a small box of this brand is $ 2.99, and the price of a large box is $3.99. Which of the following matrix expression represents the income, in dollars, received from the sale of cereal each of the three days ? {:(,"Day 1","Day 2","Day 3"),("Large",75,82,57),("Small",43,36,50):}

Luciano measured the amount of water that evaporated over a period of time from a container holding w ounces of water, where w is greater than 12. By the end of the first day, the cub had lost 2 ounces of water. By the end of the 7th day, the cup had lost an additional 8 ounces of water. By the end of the 11th day, the cup had lost half of the water that remained after the 7th day. Which of the following represents the remaining amount of water, in ounces, in Luciano's container at the end of the 11th day?

Michael needs a printing job completed. Photoperfect Print Shop charges a fixed fee of $3 for the print job and 5 cents per page. Bargain Printing charges a fixed fee of $2 for the point job and 7 cents per page. P represents the number of pages being printed, what are all values of p for which Photoperfect Print Shop's total charge is less than Bargain Printing's total charge.

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

The breakdown of a sample of a chemical compounds is represented by the function p(n)=300(0.5)^(n) , where p(n) represents the number of millligrams of the substance that remains at the end of n years. Which of the following is true? I. 300 represents the number of milligrams of the substance that remains after the first year. II. 0.5 represents the fraction of the starting amount by which the substance gets reduced by the end of each year. III. Each year the substance gets reduced by one-half of 300.

In 2014, the United States Postal Service charged $0.48 to mail a first class letter weighing upto 1oz. And $0.21 for each additional ounce. Based on these rates which function would determine the cost, in dollars, c(z), of meiling a first-class letter weighing z ounces where z is an integer greater than 1?

Direction : Resistive force proportional to object velocity At low speeds, the resistive force acting on an object that is moving a viscous medium is effectively modeleld as being proportional to the object velocity. The mathematical representation of the resistive force can be expressed as R = -bv Where v is the velocity of the object and b is a positive constant that depends on the properties of the medium and on the shape and dimensions of the object. The negative sign represents the fact that the resistance froce is opposite to the velocity. Consider a sphere of mass m released frm rest in a liquid. Assuming that the only forces acting on the spheres are the resistive froce R and the weight mg, we can describe its motion using Newton's second law. though the buoyant force is also acting on the submerged object the force is constant and effect of this force be modeled by changing the apparent weight of the sphere by a constant froce, so we can ignore it here. Thus mg - bv = m (dv)/(dt) rArr (dv)/(dt) = g - (b)/(m) v Solving the equation v = (mg)/(b) (1- e^(-bt//m)) where e=2.71 is the base of the natural logarithm The acceleration becomes zero when the increasing resistive force eventually the weight. At this point, the object reaches its terminals speed v_(1) and then on it continues to move with zero acceleration mg - b_(T) =0 rArr m_(T) = (mg)/(b) Hence v = v_(T) (1-e^((vt)/(m))) In an experimental set-up four objects I,II,III,IV were released in same liquid. Using the data collected for the subsequent motions value of constant b were calculated. Respective data are shown in table. {:("Object",I,II,II,IV),("Mass (in kg.)",1,2,3,4),(underset("in (N-s)/m")("Constant b"),3.7,1.4,1.4,2.8):} Which object would first acquire half of their respective terminal speed in minimum time from start of the motion of all were released simultaneously ?

A home designer will carpet n rooms with the same dimensions in a house using a specific type of carpeting. The designer charges using the expressions nClw, where n is the number of rooms, C is a constant with units of dollars per square meter. L is the length of the each room in meters, and w is the width of each room in meter. If a customer asks the designer to use a less expansive type oof carpating, which of the following factors in the expressions would change?

The system shown in the figure is in equilibrium, where A and B are isomeric liquids and form an ideal solution at TK . Standard vapour pressures of A and B are P_(A)^(0) and P_(B)^(0) , respectively, at TK . We collect the vapour of A and B in two containers of volume V , first container is maintained at 2 T K and second container is maintained at 3T//2 . At the temperature greater than T K , both A and B exist in only gaseous form. We assume than collected gases behave ideally at 2 T K and there may take place an isomerisation reaction in which A gets converted into B by first-order kinetics reaction given as: Aoverset(k)rarrB , where k is a rate constant. In container ( II ) at the given temperature 3T//2 , A and B are ideal in nature and non reacting in nature. A small pin hole is made into container. We can determine the initial rate of effusion of both gases in vacuum by the expression r=K.(P)/(sqrt(M_(0))) where P= pressure differences between system and surrounding K= positive constant M_(0)= molecular weight of the gas If vapours are collected in a container of volume 8.21 L maintained at 3 T//2K , where T=50 K , then the ratio of initial rate of effusion of gases A and B is given as