In the following, write an expression in terms of the
given variables that represents the indicated quantity:
a. The cost of having a plumber spend h hr at your
house if the plumber charges $30 for coming to the
house and $x per hour for labor
b. The amount of money in cents in a jar containing
some nickels and d dimes and some quarters if there
are 4 times as many nickels as dimes and twice as many
quarters as nickels
c. The sum of three consecutive integers if the greatest
integer is x
cost: 30 + x*h
money: 10d + 5*4d + 25(2*4d)) = 230d
sum: x-2 + x-1 + x = 3x-3
a. The cost of having a plumber spend h hr at your house if the plumber charges $30 for coming to the house and $x per hour for labor:
The expression representing the cost would be:
Cost = $30 + ($x/h) * h
b. The amount of money in cents in a jar containing some nickels and d dimes and some quarters if there are 4 times as many nickels as dimes and twice as many quarters as nickels:
Let n be the number of nickels and q be the number of quarters. Since there are 4 times as many nickels as dimes, the number of nickels would be 4d. And since there are twice as many quarters as nickels, the number of quarters would be 2(4d) = 8d.
The value in cents of nickels can be represented as 5n, dimes as 10d, and quarters as 25q.
The expression representing the amount of money in the jar would be:
Amount = 5(4d) + 10d + 25(8d)
c. The sum of three consecutive integers if the greatest integer is x:
Let the three consecutive integers be x-1, x, and x+1.
The expression representing the sum of these three integers would be:
Sum = (x-1) + x + (x+1) = 3x
a. The cost of having a plumber spend h hr at your house can be represented as the sum of the cost for the plumber's visit plus the cost for the labor. The plumber charges $30 for coming to the house, which is a fixed cost. The cost for the labor is calculated by multiplying the hourly rate, represented by x, by the number of hours, h. Therefore, the expression that represents the cost is:
Cost = $30 + x * h
b. To calculate the amount of money in cents in a jar containing nickels, dimes, and quarters, we need to determine the value of each coin and then sum up their quantities.
Given that there are 4 times as many nickels as dimes and twice as many quarters as nickels, we can express the number of nickels, dimes, and quarters as follows:
Number of nickels = 4 * dimes = 4d
Number of quarters = 2 * nickels = 2 * (4d) = 8d
The value of each coin in cents is as follows:
Nickels = 5 cents
Dimes = 10 cents
Quarters = 25 cents
To calculate the total amount of money in cents, we multiply the value of each coin by its quantity and sum them up:
Amount in cents = (5 * (4d)) + (10 * d) + (25 * (8d))
Simplifying the expression:
Amount in cents = 20d + 10d + 200d
Amount in cents = 230d
Therefore, the expression that represents the amount of money in cents is:
Amount in cents = 230d
c. The sum of three consecutive integers can be expressed by adding the integers together. However, since we are given that the greatest integer is x, we need to determine the other two consecutive integers based on this information.
Let's assume the three consecutive integers are x - 1, x, and x + 1.
The sum of these three integers can be calculated as follows:
Sum = (x - 1) + x + (x + 1)
Simplifying the expression:
Sum = 3x
Therefore, the expression that represents the sum of three consecutive integers is:
Sum = 3x
a. Cost = $30.00 + h x $x
$30 initial fee plus number of hours times the cost per hour.
b. The value of the dimes can be written as $0.10 x d (the number of dimes). The number of nickels can be written as 4 times the number of dimes (4d) but the value is written as $0.05 x 4d. The number of quarters is twice the number of nickels which is four times the number of dimes. So, the number of quarters is (8d). The value of the quarters is $0.25 x 8d.
The equation would be: ($0.10 x d) + ($0.05 x 4d) + ($0.25 x 8d)=$_____. You could, then factor out the d (number of dimes), multiply the values($0.10, $0.05 and $0.25) times their respective quantity multiplier (1, 2, 4). This gives you the amount = $2.30 x d (for every one dime, you have enough dimes, nickels, and quarters to equal $2.30, so count the dimes and multiply by $2.30.
c. Sum = x + (x-1) + (x-2)= 3x-3