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user100 [1]
3 years ago
5

At a baseball game, a vender sold a combined total of 170 sodas and hot dogs. the number of hot dogs sold was 50 less than the n

umber of sodas sold. find the number of sodas sold and the number of hot dogs sold
Mathematics
1 answer:
Juliette [100K]3 years ago
8 0

Let the number of sodas sold be x and the number of hotdogs sold be y. We can assemble a system of equations from the information given and solve.


x+y=170 (We know that soda + dogs is 170)

x-50=y (We know that dogs is equal to 50 less than sodas)


We can use substitution to solve this system of equations.

x+y=170

Sub in the value of y from the second equation

x+(x-50)=170

2x-50=170

2x=220

x=110


We now know the number of sodas sold was 110. Lets now plug this value into the equation to solve for y.

x+y=170

110+y=170

y=60


So, there were 60 hotdogs sold and 110 sodas sold.

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A fence is to be built to enclose a rectangular area of 450 square feet. The fence along three sides is to be made of material t
Mila [183]

Answer:

The short side is _15___ft and the long side is ___30___ ft.

Step-by-step explanation:

As fence is built in a rectangular area, so we can consider

Let

 x be the length of the rectangle  

y be width of the rectangle

Given area of rectangle is = 450 ft²

Formula for area of rectangle = Length x width  

     450 ft² =  xy  

Solve for y

y = 450/x            

now according to given condition  

three sides of the fence costs $5 per foot and for the fourth side costs$15 per foot.

We have two condition either the fourth side be x or y

So condition 1:  Three sides =(x,y,x)       4-th side = y.

So  we can write as 5x,5y,5x  and  15 y  

Cost C = 5x +5y+5x+15y

         = 10x+ 5y+15y

         = 5(2x+y) +15y----------------equation 1

           = 10x +20y

Adding value of y 450/x

        = 10x + 20(450/x)

  = 10x + 9000/x

For minimum cost, we can consider the cost to be 0

 0 = 10x + 9000/x

Dividing and multiplying by -x/x

0 = -10 +9000/x²

10 = 9000/x²

 10x² = 9000/  

 x²= 900

x = 30

so y = 450/x = 450/30= 15 ft  

so adding the values of x and y in equation 1 we will have

cost C= 5(2x+y) +15y----------------equation 1

cost is          = 5(2(30)+15) +15(15)

                      =  $600 is the cost  

X= 30 y =15

So condition 2:  Three sides =(y,x,y)       4-th side = x.

So  we can write as 5y,5x,5y  and  15 x

Cost C = 5y +5x+5y+15x

         = 5x+ 10y+15x

         = 5(x+2y) +15x----------------equation 2

           = 20x +10y

Adding value of y= 450/x

        = 20x + 10(450/x)

  = 20x + 4500/x

For minimum cost, we can consider the cost to be 0

 0 = 20x + 4500/x

Dividing and multiplying by -x/x

0 = -20 +4500/x²

20 = 4500/x²

 20x² = 4500

 x²=  4500/20= 225

x = 15

so y = 450/x = 450/15= 30 ft  

so adding the values of x and y in equation 2 we will have

cost C= = 5(x+2y) +15x----------------equation 2

cost is          = 5(15+2(30) +15(15)

                      =  $600 is the cost  

y= 30 x=15

so from both conditions satisfy the cost and the two sides are known as length and width

so dimension will be 15 ft by 30 ft  

7 0
3 years ago
80 points if you answer this question!
Neporo4naja [7]
Total amount of Carbon-14
= 12 - (0.00012 \times 5000)
= 12 - 0.6
= 10.4
=C

Full marks answer

8 0
3 years ago
Read 2 more answers
Please help me with number 9
Mrrafil [7]
The answer is 8 pints
8 0
3 years ago
Michael is trying to write the algebraic expression for the following word phrase: the quotient of 6 and the sum of 5 and y? Mic
gizmo_the_mogwai [7]

Answer:

Error: He multiplied 6 by 5 + y instead of divided 6 by 5 + y

Correct solution: 6 ÷ (5 + y)

Step-by-step explanation:

- <em>Lets revise some words of some operations in mathematics</em>

# The sum ⇒ (+) Add

# The difference ⇒ (-) subtract

# The product ⇒ (×) multiply

# The quotient (answer of division) ⇒ (÷) divide

* <em>Lets solve the problem</em>

- Michael is trying to write the algebraic expression for the following

 word phrase:

 the quotient of 6 and the sum of 5 and y

- <u><em>Lets explain that:</em></u> the quotient means the answer of division so he

 wants to divide a quantity by another one

∵ The first quantity is 6

∵ The second quantity is the sum of 5 and y

- He wants to divide 6 by (5 + y)

∴ The expression is 6 ÷ (5 + y)

* Error: He multiplied 6 by 5 + y instead of divided 6 by 5 + y

* Correct solution: 6 ÷ (5 + y)

4 0
3 years ago
Write the prime factorization of 500 using exponents.
vekshin1
2 x 2 x 5 x 5 x 5

2^2 x 5^3
5 0
3 years ago
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