At the holiday valley ski resort, skis cost $16 to rent and snowboards cost $19. If 28 people rented on a certain day and the resort brought in $478, how many skis and snowboards were rented?

Answers

Answer 1

Answer:

Answer:

$18$ skis and $10$ snowboards were rented.

Step-by-step explanation:

Let the number of skis rented be $x$ and the number of snowboards rented be $y$ .

If a total of $28$ people rented on a certain day, then the total number of skis and snowboards rented that particular day is also $28$ .

This gives us the equation

$x+y=28...eqn(1)$ .

If skis cost $ $16$ , then $x$ number of skis cost $ $16x$ .

If snowboards cost $ $19$ , then $y$ number of snowboards cost $ $19y$ .

The total cost will give us another equation,

$16x+19y=478...eqn(2)$

From equation (1),

$y=28-x...eqn(3)$ .

We put equation (3) into equation (2) to get,

$16x+19(28-x)=478$

We expand the brackets to obtain,

$16x+532-19x=478$

We group like terms to get,

$16x-19x=478-532$

This implies that,

$-3x=-54$

We divide both sides by $-3$ to get,

$x=18$

We put $x=18$ into equation (3) to get,

$y=28-18$

$y=10$

Therefore $18$ skis and $10$ snowboards were rented.

Answer 2

Answer:

Final answer:

To solve this problem, you can set up a system of equations where one equation represents the total number of skis and snowboards rented, and the other represents the total cost of those rentals. By solving this system, you can determine the number of skis and snowboards rented.

Explanation:

This problem is a classic example of a system of linear equations. Let's denote the number of skis rented as x and the number of snowboards rented as y. From the problem, we know that:

x + y = 28 (The total number of skis and snowboards rented is 28)
16x + 19y = 478 (The total income from skis and snowboard rentals is $478)

By solving these two equations, we can find the values of x and y which represent the number of skis and snowboards rented respectively.

Learn more about System of linear equations here:

brainly.com/question/20379472

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If $396 is invested at an interest rate of 13% per year and is compounded continuously, how much will the investment be worth in 3 years?

Answers

if the interest is compound (yearly) then is calculated by
A = P (1+r)^(t)

then after 3 years the investment will worth

396(1.13)^3 = $571.38

Answer:

$\$584.88$

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^(rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=3\ years\n P=\$396\n r=0.13$

substitute in the formula above

$A=\$396(e)^(0.13*3)=\$584.88$

Julie has 1,429 reward points from shopping at an online store. She uses the points to buy gift cards for free cups of coffee. Each card costs 150 points.What is the greatest number of gift cards Julie can buy?
How many reward points will she have left?

Answers

Answer:

Julie can buy 9 gift cards and will have 79 reward points left over

Step-by-step explanation:

If you divide 1,429 by 150, the number before the decimal, 9, is how many she can buy without exceeding her limit

Then, multiply 9 and 150 to see how many points 9 gift cards is worth (1350)

Subtract 1429-1350 to find the leftover points (79)

The number x of stereo speakers a retail chain is willing to sell per week at a price of p dollars is given by. Find the supply and instantaneous rate of change of supply when the price is 75 dollars?

Answers

Answer:

Please find below the complete question:

The number x of stereo speakers a retail chain is willing to sell per week at a price of p dollars is given by x = 80 $√(p+27)$ − 410. Find the supply and instantaneous rate of change of supply when the price is 75 dollars.

Supply = 398

Instantaneous rate of change of supply $=3.96$

Step-by-step explanation:

$x=80√(p+27) -410$

Supply when price = $75

$x=80√(75+27) -410 = x=80√(102) -410\n\nx = 80(10.1) -410= 808-410\n\nx = 398$

Supply = 398 stereo speakers

To get the instantaneous rate of supply, we differentiate the supply, x, with respect to price, p

$(dx)/(dp) = (d)/(dp)(80√(p+27) -410)\n\n(dx)/(dp) = (d)/(dp)(80(p+27)^(1/2) -410)$

Using chain rule, we have

$(x)/(y) (dx)/(dp)=(d)/(dp)( 80(p+27)^(1/2)) - (d)/(dp)(410) \n\n(dx)/(dp)=80((1)/(2))(p+27)^(-1/2) - 0\n\n(dx)/(dp)=(40)/(√(p+27) ) \n$

At p = $75

$(dx)/(dp)=(40)/(√(75+27) )=(40)/(√(102) )\n\n(dx)/(dp)=(40)/(10.1) = 3.96\n\n(dx)/(dp)=3.96$

The question is not complete and the complete question says:

The number x of stereo speakers a retail chain is willing to sell per week at a price of p dollars is given by x=80√(p+27) − 410 Find the supply and instantaneous rate of change of supply when the price is 75 dollars

Answer:

A) Approximately 398 stereo speakers

B) Instantaneous rate of change = 3.961

Step-by-step explanation:

From the question, the number of speakers is given as;

x=80√(p+27) − 410

A) Thus at a price of $75,

The amount supplied will be;

x = 80√(75+27) − 410

x = 80√(102) - 410

x = (80 x 10.0995) - 410

x = 807.96 - 410 = 397.96 ≈ 398 stereo speakers

B) The instantaneous rate of change is given as;

dx/dp of the supply equation.

Thus, let's rearrange the supply equation first before differentiating.

So, x = 80√(p+27) − 410

x = 80[(p +27)^(1/2)] - 410

So, dx/dp = [(80 x 1/2) (p + 27)^(-1/2)]

dx/dp = 40/√(p+27)

So, at price of $75,

dx/dp = 40/√(75+27) = 40/√102

= 40/10.0995 = 3.961

The student council is selling cookies.They buy the cookies from the store for .55 cents each.They sell the cookies for $1 each.What is the percent of markup

Answers

Answer:

The percentage of the markup is 82%

Step-by-step explanation:

In this question, we are asked to calculate the percentage of mark up. This is simply calculating the percentage of the profit margin.

firstly to be able to calculate this percentage, we need to know the value of the profit margin itself.

mathematically, the profit margin is selling price - cost price

From the question, the selling price is $1 while the cost price is 55 cents

The profit margin is thus $1 - 55 cents = 45 cents

We now proceed to calculate the percentage profit

mathematically, that is profit/cost price * 100%

That would be 45 cents/55 cents * 100 = 9/11 * 100% = 81.8 approximately 82%

6^x+8=17^2x-2 can I have help

Answers

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If you invest $2,000 today in a bank that gives you a 4 percent annual interest rate, which of these items can you buy in seven years?

Answers

Just the Mountain bike, cause 4% of $2000 is, $80. and $80 for each year for 7 years make $560. now after 7 years your bank account has $2560. Therefore, you can buy a mountain bike, and have $60 left over, if there is no tax included. But if there is tax, your going to be still short by $115.(calculated according to florida's tax, that is 7%.) Anyways if the tax is over 2% you cant get that bike.

All of them

put this in a calculator: 2000*20%*7 then take away the prices or bills and thats how much money is left after the shopping spree

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