Mathematics High School

Peter is renting two kinds of rafts for a vacation company. One type seats 3
people and the other seats 5 people. If 53 people are using the vacation
company and he rents 13 rafts, how many of each type of raft does he rent?

Answers

Answer 1

Answer:

Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.

Step-by-step explanation:

Let [tex]x[/tex] denote the number of rafts seating 3 people and [tex]y[/tex] the number of rafts seating 5 people. The total number of rafts is 13, so [tex]x+y=13[/tex]. We can also assume that every raft is filled to the brim (it isn't stated explicitly though, but it's probably the intention of the question maker), so [tex]3x+5y=53[/tex].

It's always a good idea to put these equations under each other:

[tex]\left \{ {{x+y = 13} \atop {3x+5y=53}} \right.[/tex]

We can subtract the first equation three times from the second one to obtain [tex](3x+5y)-3(x+y) = 53 - 3(13)\\3x-3x + 5y - 3y = 53 - 39\\2y = 14\\y=\frac{14}{2} = 7[/tex]

Now, substitute this found value for [tex]y[/tex] into [tex]x+y = 13[/tex] and we see that [tex]x=6[/tex]. We are now done: Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.

Related Questions

Find the quotient.
52.06 divided by 1.9

Answers

Answer:

27.4

Step-by-step explanation:

First multiply the numerator and denominator by 10

Then write the problem in long division format

Then divide 52 by 19 and get 2

Then multiply the quotient digit (2) by the divisor 19

Then subtract 38 from 52

Then bring down the next number of the dividend

Then divide 140 by 19 to get 7

Then multiply the quotient digit (7) by the divisor 19

Then subtract 133 from 140

Then add a decimal point to the solution

Then bring down the next number of the dividend

Then divide 76 by 19 to get 4

Then multiply the quotient digit (4) by the divisor 19

Then subtract 76 from 76

The solution for long division for 52.06./1.9 is 27.4

27.4

Answer:

quotient is 27.4

Step-by-step explanation:

your welcome;)

Tito's Mom is 38, his father is 42, his sister is 15 he is 13 and has twin
brothers aged 6. What is the median age of Tito's family?

Answers

Answer:

Step-by-step explanation:

Dad: 42

Mom: 38

Sister: 15

Tito: 13

Twin 1: 6

Twin 2: 6

(15+13)/2 = 28/2= 14 years old

what is k + 1 3 = 5 1/8

Answers

The answer is k=-63/8

witch answer should I pick .

Answers

You should pick none of the above

Answer:

34 and 10

Step-by-step explanation:

8.5/.5=17

17x2=34

2.5/.5=5

5x2=10

10 and 34

What are the values of x and y in the figure

Answers

Answer:

I'm pretty sure 8

Step-by-step explanation:

55 videos to 77 videos

Answers

Answer:

The ratio is 55:77

Step-by-step explanation:

what fraction in lowest terms represents the valur of c in the equation 3(4x -6) = -3(5 -2x)

Answers

Answer:

3(4x - 6) = - 3(5 - 2x)

12x - 18 = - 15 +6x

12x - 6x = - 15 +18

6x = 3

x = 1/2

HELP I NEED HELP ASAP

Answers

9514 1404 393

Answer:

  A. exponential; constant % rate of change

Step-by-step explanation:

Each round has 50% of the players of the previous round, so the rate of change is a constant percentage. That makes the function a decaying exponential function, matching choice A.

Find the sale price of a $15 item after a 20% discount.

Answers

Answer:

12

Step-by-step explanation:

find 20% of 15 and then take that away from the 15

What you would do is X/15 and 20/100 Now cross multiply so x100 = 15 x 20 15 x 20 = 300, but you need to have x by it self so 300/100 = 3

Hope I said everything right and make sure to double check my math. Have a great day!

Given that f(x)= x^2-3/2 a)find f(3) b) find f

Answers

Answer:

Step-by-step explanation:

f(3)=3^2-3/2=3*3-3/2=9-3/2=18/2-3/2=15/2

The HCF of 36 72 63
The LCM of 8 9 12​

Answers

LCM of 8,9,12 is 72

HCF of 36 72 63 is 3

Find the shaded area. 12 cm 18 cm 8cm 8cm

Answers

You start with finding area of both then subtracting area of white box.
12x18=216
8x8=64
216 - 64 = 152
So the area of the shaded area = 152 cm^2

Step-by-step explanation:

152 cm square is ur answer

Give an example of a proportion that uses the numbers 2, 3, 4 and 6.

Answers

Give an example of a proportion that uses the numbers 2, 3, 4 and 6.

2:3 is the same as 4:6

Proportion says that two ratios (or fractions) are equal.

Does anyone know this? I can't seem to figure this one out at all.

Answers

Answer:

a = 5, b = -1

Step-by-step explanation:

Simplify the left side.

Multiply both numerator and denominator by the conjugate of the denominator:

(√3 - 1)/(√3 + 1) = (√3 - 1)(√3 - 1)/(√3 - 1)(√3 + 1) =(√3² - 2√3 + 1)/(3 - 1) =(10 - 2√3)/2 = 5 - √3

Compare this to the right side to get:

5 - √3 = a + b√3a = 5, b = -1

Which graph shows a solution of approximately (1.2, -1.3)

Answers

Answer:

D

Step-by-step explanation:

please help!

Create an equation for the following situation and find the value of x.

8 more than 2 times a number x, all divided by 5 equals 2.

Answers

Answer:

8+2x/5=2

2x/5=2-8

2x/5=-6

2x=-6x5

2x=-30

x=-30/2

x=-15

Step-by-step explanation:

how do you solve this

Answers

Pretty sure it’s -8

What is the longest side of the triangle with vertices of (1,4), (3,4), and (3,6)?​

Answers

Answer the answer to your question is :
(2,5)

OLEASE HELPP ILL GIVE 30 points

Answers

Answer:CHope this helps!! ♥︎

Answer: The correct answer is c

Step-by-step explanation: Can I get brainliest for the correct answer pls and you're welcome but I'm not being rude.

Please help me out fast. And make sure to Write and solve an inequality. Or it isn't right.

Answers

Answer:

addition or multiplication?

Step-by-step explanation:

Answer:

6x + 45 > 240

Step-by-step explanation:

I will give in a min. You need it urgently right. So you can have the answer for now!!!

I NEED HELP PLEASE!!!

Answers

Answer:

hardhard

Step-by-step explanation:

Choose the equation that shows the relationship of 80%, x, and 100.

Answers

Answer:

chipset buy showroom de en inglés

Find the value
of 6y^2 - 24y - 51 when y=-2

​

Answers

Answer:

21

Step-by-step explanation:

6(y^2) - 24y -51 = 6 4 - 24y - 51

(6 4) - (24y) - 51 = 24 - -48 - 51

(24 - -48) - 51 = 72 - 51

72 - 51 = 21

taking diagnostic ill give brainliest

Answers

The function is decreasing on the interval (-∞,∞)

This means that, throughout the whole graph, the slope is negative.

Answer:

g

Step-by-step explanation:

g

I NEED SOME HELP AGAIN PLS

Answers

Answer:

The y-intercept is (26, 0)

Step-by-step explanation:

The Y intercept is the point at which the line crosses the  y-axis, or when x is equal to zero. Here when x = 0, y = 26. So the y-intercept is (26, 0). They want to trick you into choosing the slope is -1/6, but that is wrong because id you look at the x-axis it is not going by 1's.

(26, 0) this is the graphingy intercept is (26,0)

I need someone to solve these equations step by step by today, please help


3​x​ + 2 + ​x​ = ​x​ + 5

6 − ​x​ − 3 = 4(​x​ − 2)

4​x​ − 2 − 2​x​ = ​x​ − 5


−(​x​ + 3) = 2​x​ − 6

Answers

Answer:

x=1

Step-by-step explanation:

You need to add the Numbers with an x together as if they were racist on each side so you'd have

4x+2 = x+5

Then to move them to either side you must do the opposite symbol of what they are so if their positive their now negative

4x-x=-2+5

then add them together

3x= 3

then divide the normal number with the number with the x

x=1

For the next problem you Multiply thr number that are in the paranthases by the number on the outside so

6-x-3 = 4(x-2)

6-x-3= 4x-8

then copy the steps that I told you from last problem

-9-x=4x-8

then

-9+8=x+4x

thenn

-1=5x

divide

0.2-=X

Express the interval using inequality notation,
-4,5

Answers

Answer:

First you mark me Brainlyist

Step-by-step explanation:

Then you you use the intervol of I don’t know then you ask someone else

WILL GIVE BRAINIEST!!!!!

Answers

Answer:

x=2

Step-by-step explanation:

Which of the following is a quadratic function?
f(x) = 0x + 3x - 6
f(x) = 2x + 5
f(x) = 3 - 4x^2
f(x) = 2^x

Answers

Answer:

f(x) = 3 - 4x^2

Step-by-step explanation:

Quadratic Equation form:   f(x) = ax² + bx + c

Quadratic function has a x (variable) with and exponent of 2.

They also leave a curve line on a coordinate plane. As you can see on the picture. ↓

hey can you guys please confirm my answer, i got B

Answers

B is correct since there is one output for every input !!


have a great day :))
B is correct. You’re smart.
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