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e-lub [12.9K]
2 years ago
5

A new miniature golf and arcade opened up in town. For convenient ordering, a play package is available to purchase. It includes

two rounds of golf and 20 arcade tokens, plus $3.00 off the regular price. Stacey and her six friends are purchasing this package. Let g represent the cost of a round of golf, and let t represent the cost of a token. Write two different expressions that represent the total amount this group spent.
Mathematics
1 answer:
ruslelena [56]2 years ago
7 0

Answer:

a. 7(2g + 20t –3)

b. 14g + 140t – 21

Step-by-step explanation:

a. The first expression 7(2g + 20t  – 3)

Stacey and her six friends implies that we have 7 members in the group.

Therefore, the expression above implies that each member of the group has to pay for two rounds of golf and 20 tokens will be discounted $3.00.

The expression (2g + 20t –3) represents the quantity of cost of each friend and this is multiplied by 7 to obtain this first expression, i.e. 7(2g + 20t –3).

b. The second expression 14g + 140t – 21

The simple interpretation of this expression us that deducting $21 from the to total bill which is 14 games of golf plus 140 tokens is equal to the total amount this group spent.

Therefore, this second expression is obtained by simply opening the bracket in the first expression by multiplying 7 by each of the what is in the bracket.

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There are some goats, cows, and sheep on a farm. 2/5 of the animals were goats. There are 3 times as many sheep as cows. If ther
svetlana [45]

Answer:

180

Step-by-step explanation:

First thing to do is to get all the animals in terms of cows, since that is our main unknown.  All the other animals' numbers are based on cows.  So let's call cows "x".  Then sheep is 3 times the number of cows, so sheep is 3x.  The number of goats is 45 more than the number of cows, so goats is x + 45.  Let's say, for the sake of ease, that the number of animals is "a".

Here's what we have so far:

# of animals: a

# of cows: x

# of sheep: 3x

# of goats: x + 45

We are told that 2/5 of the animals are goats.  In an equation, that is:

2/5 (animals) = goats, where the word "of" means to multiply, and the word "are" is the equals sign.  Filling in from our key above:

\frac{2}{5}a=x+45

That says that 2/5 of the animals are goats when goats is x + 45.

If 2/5 of the animals are goats, then 3/5 of the animals have to be cows and sheep.  In an algebraic equation:

\frac{3}{5}a=x + 3x.  

Let's go back to the first equation and get rid of the fraction by multiplying everything by 5.  When we do that we get

2a = 5(x + 45) so

2a = 5x + 225

Now let's get rid of the fraction in the second equation by multiplying everything by 5.  When we do that we get

3a = 5(x + 3x) or

3a = 5(4x) so

3a = 20x.  Solve that equation for a.

a=\frac{20}{3}x

Now that we have a in terms of x, we can sub that value in for a in the first equation to solve for x, the number of cows:

2(\frac{20}{3}x)=5x+225 and, simplifying:

\frac{40}{3}x=5x+225 and

\frac{40}{3}x-5x=225.  Get rid of the fraction here by multiplying everything by 3:

40x - 15x = 675 and

25x = 675 so

x = 27

That means that there are 27 cows.

Sheep is 3 times that, so there are 81 sheep.

Goats is 45 more than that, so there are 72 goats.

The total number of animals then is 27 + 81 + 72 which is 180.  Let's check that to see if the number of goats, 72, is 2/5 of 180.

\frac{2}{5}(180) = 72

So we got it!  Yay!  That was hard!!

7 0
2 years ago
a basketball player looks directly at the rim that is 10 feet high. the angle of elevation from her eye level, which is 6feet ab
Aneli [31]
Her horizontal distance to the rim satisfies the ratio
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6 0
3 years ago
Please show me the work!
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Answer:

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Step-by-step explanation:

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Rate of change of volume dV/dt = dV/dr * dr/dt

dV/dr = 3(4/3πr²)

dV/dr = 4πr²

dV/dr = 4π(2)²

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If V = 72cm²/s

72 = 16π*dr/dt

dr/dt = 72/16π

dr/dt = 9/2π cm/s

Hence the radius is changing at  9/2π cm/s

6 0
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Mademuasel [1]

Answer:

Every 200 visitors, the visitor will receive all 4 gifts.

Step-by-step explanation:

With the given numbers, the lowest common number would be 200.

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Answer:

c

Step-by-step explanation:

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