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Mandarinka [93]
2 years ago
7

Kim and Melody are selling popcorn buckets for a school fundraiser. Customers can buy small buckets or large buckets. Kim sold 3

small buckets and 14 large buckets of popcorn for a total of $206. Melody sold 11 small buckets and 11 large buckets of popcorn for a total of $231. What is the cost for a small bucket and a large bucket of popcorn?
Mathematics
1 answer:
Papessa [141]2 years ago
4 0

Answer:

The cost of

A small bucket = x = $8

A Larger bucket = y = $13

Step-by-step explanation:

Let the cost of

A small bucket = x

A Larger bucket = y

Kim sold 3 small buckets and 14 large buckets of popcorn for a total of $206.

3x + 14y = 206... Equation 1

Melody sold 11 small buckets and 11 large buckets of popcorn for a total of $231.

11x + 11y = 231.... Equation 2

What is the cost for a small bucket and a large bucket of popcorn?

3x + 14y = 206... Equation 1

11x + 11y = 231 ....... Equation 2

We solve using Elimination method

Multiply Equation 1 by 11 and Equation 2 by 3 to Eliminate x

33x + 154y = 2266.... Equation 3

33x + 33y = 693....... Equation 4

We subtract Equation 4 from Equation 3

121y = 1573

y = 1573/121

y = $13

Solving for x

3x + 14y = 206... Equation 1

3x + 14 × 13 = 206

3x + 182 = 206

3x = 206 - 182

3x = 24

x = 24/3

x = $8

Hence, the cost of

A small bucket = x = $8

A Larger bucket = y = $13

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Find an equation of variation where y varies directly as x and y = 7 when x = 0.5 .
Alisiya [41]

Answer:

y = 14x

Step-by-step explanation:

Use the direct variation equation, y = kx

Plug in 7 as y and 0.5 as x, and solve for k:

y = kx

7 = k(0.5)

14 = k

Plug this into the equation:

y = kx

y = 14x

So, the equation of variation is y = 14x

4 0
3 years ago
EMERGENCY QUESTION! No Decimal answers plz!
telo118 [61]

Answer:

1,145,375 cm³

Step-by-step explanation:

Like with an earlier question you had, there is a chunk missing. If that chunk was filled in, this would be a 205 * 70 * 85 rectangular prism.

205 * 70 * 85

17,425 * 70

1,219,750

The cut out chunk is a 25 * 70 * 85 triangular prism.

1/2 (25 * 70 * 85)

1/2(2,125 * 70)

1/2(148,750)

74,375

Now that we know what the cut-out chunk is, subtract that from the first value we got.

1,219,750 -74,375

1,145,375 cm³

The volume of the Canadian Post mailbox is 1,145,375 cm³.

8 0
2 years ago
Read 2 more answers
The sum of two consecutive odd integers is 236. What is the smaller integer?
Kryger [21]
HEY there,

236/2=117 

117 enn odd number 

117+117=236

1,3,7 are odd number so 

hope this helped you 

Plz mark brainliest if you want (;

5 0
3 years ago
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(a) Derive an equation of the line passing through the points A(0, 545) and B(4, 726). (Let t be the independent variable and y
a_sh-v [17]

Answer:

The equation of the line is y=45.25t+545

Step-by-step explanation:

The general for of a line is:

y=mt+n       (1)

where:

m is the slope of the line and m is the intercept with the axis of the dependent variable, y in this case.

In order to obtain the value of the slope (m) we can use the corresponding slope formula:

m=\frac{y_{2}-y_1 }{t_2-t_1}         (2)

where t_1, t_2, y_1 and y_2 are the corresponding coordinates of the given points. In this case:

t_1=0\\t_2=4\\y_1=545\\y_2=726\\

Substituting these values in equation (2) we obtain:

m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25

Hence, the line equation is now:

y=45.25t+n     (3)

Now to obtain the value of n you can follow two options:

  1. You can substitute one of your points, A or B, in equation (3). In this way, you will obtain an equation where the variable is n

Note that for this question, it is easier to select point A because of having the independent variable equals to zero t=0. Hence, substituting point A in equation (3):

45.25*0+n=545\\n=545

Therefore, the line equation is: y=45.25t+545

The second option to find n is to think of the meaning of the <em>intercept</em>. The <em>intercept </em>of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that n is equal to 545.

See the attachment for a plot of the line.

7 0
3 years ago
What is the domain of f/g, given f(x)=x+2 and g(x)=x-7?
kodGreya [7K]

Answer:

(-∞,7) U (7,∞)

Step-by-step explanation:

f(x)= x+2

g(x) = x-7

\frac{f(x)}{g(x)} =\frac{x+2}{x-7}

Here we have x-7 in the denominator

To find domain we set the denominator =0  and solve for x

x-7=0

Add 7 on both sides

x=7

x=7 makes the denominator 0 that is undefined

So we ignore 7 for x

Hence domain is

(-∞,7) U (7,∞)

5 0
2 years ago
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