The museum charges $12.50 for youth admission and $17.50 for adults. One day the museum collected $1535 from a total of 110 youths and adults. How many admissions of each type were sold?

Answers

Answer 1

Answer: x - young
y - adult

$12.50x+17.50y=1535\n x+y=110\n\n 12.50x+17.50y=1535\n x=110-y\n\n 12.50(110-y)+17.50y=1535\n 1375-12.50y+17.50y=1535\n 5y=160\n y=32\n\n x=110-32\n x=78$

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Fourteen is 50% less than what number?

Answers

21 since 14 x 1.5 is 21

Sarah saved $15 buying the dressat a 20%-off sale. What was the
regular price of the dress?

Answers

Answer:

$18

Step-by-step explanation:

since she saved 20% you turn the percentage into a decimal which is .20 then multiply it by 15 because that's how much she saved and you get $3 which you add to $15 and you get the regular price which is $18

The price is $18 because you change the 20% to .20 and multiply it by 15 which gives you $3and then you add which gives you your answer.

The amount $3. 80 is 4% of what price? a. $7. 80 b. $15. 20 c. $95. 00 d. $97. 20

Answers

Final answer:

The original price for which 4% equals to $3.80 is $95.00 (option c). This was calculated by dividing the given percentage amount ($3.80) by the percentage rate (0.04, which is 4% in the decimal form).

Explanation:

The question is asking us to find out what price $3.80 is 4% of. To answer this, we need to solve for the unknown price, which we'll call 'X'. In the context of this problem, we set up the equation 0.04*X = $3.80. To solve for 'X', we divide $3.80 by 0.04 to find out the original price. Therefore, X equals $95.00, which means that $3.80 is 4% of $95.00. Thus, the answer is c. $95.00.

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A team t-shirt costs $3 per adult and $2 per child. On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, and the total money collected was $275. Which of the following options represents the number of children and the number of adults who purchased team shirts that day, and the pair of equations that can be solved to find the numbers? A.) 75 children and 25 adults
Equation 1: a + c = 100
Equation 2: 3a − 2c = 275

B.) 75 children and 25 adults
Equation 1: a + c = 100
Equation 2: 3a + 2c = 275

C.) 25 children and 75 adults
Equation 1: a + c = 100
Equation 2: 3a − 2c = 275

D.) 25 children and 75 adults
Equation 1: a + c = 100
Equation 2: 3a + 2c = 275

Answers

Answer:

Option D is correct.

Step-by-step explanation:

A team t-shirt costs $3 per adult and $2 per child.

Let the number of children be = c

Let the number of adults be = a

A team t-shirt costs $3 per adult that is 3a and $2 per child that is 2c, also given is that the total money collected is $275, so equation becomes:

$3a+2c=275$

On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, equation becomes: $a+c=100$

Now to know the number of children and adult, we can check by plugging in the values from options provided.

25 children and 75 adults = 25(2)+75(3)=50+225 =275

Rest options do not fulfill the requirements, so Option D is correct.

The answer is:

25 children and 75 adults
Equation 1:a + c=100
Equation 2: 3a + 2c=275

Have a nice day!

For what value of k are the two lines 2x + ky = 3 and x + y = 1 parallel?

Answers

Remember that: the slope-intercept form of a
line is
1 of 3
y= m. x+c
where m is the slope of the line.
The equation for the first line is 2x + ky = 3
To find the slope, we simply have to rewrite the
given equation into its slope-intercept form.
Start by subtracting 2a from both sides
KY
=
-22 +3
Divide both sides by k
y =
2
•It
3
K
K
The above equation is now in slope-intercept
form, and the coefficient of a is -2/k, so that
is the slope for the first line.

Final answer:

The two lines 2x + ky = 3 and x + y = 1 are parallel when the value of k equals 2, as parallel lines have equal slopes.

Explanation:

To determine the values of k for which these two lines are parallel, we need to first understand that parallel lines have the same slope. The slope is the coefficient, or number, with the variable x in the equation of the line.

The first line 2x + ky = 3 can be rewritten in slope-intercept form (y = mx + b) as:

y = -2/kx + 3/k

Here, the slope is -2/k. The second line x + y = 1 can also be rewritten in slope-intercept form as:

y = -x + 1

Here, the slope is -1.

Since the slopes of parallel lines are equal, we equate -2/k to -1:

-2/k = -1

Solving this equation, we find that k = 2. So, the two given lines are parallel when k = 2.

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Tony is standing at sea level. From his location, the angle of elevation of the top of Blue Mountain is 23°. Staying at sea level, he walks 220 yards toward the mountain. The angle of elevation of the top is now 27°. Find the height of Blue Mountain. Round intermediate results to 3 decimal places and the final answer to 1 decimal place.