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3 years ago

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Henri bought a swim suit at a cost of $8. Which statements are true regarding the cost of the suit? Select three options. If the

selling price is marked up by 25 percent, the new price will be $10. If the selling price is marked up by 40 percent, the new price will be $7.50. If the selling price is marked up by 55 percent, the new price will be $5.50. If the selling price is marked up by 70 percent, the new price will be $13.60. If the selling price is marked up by 75 percent, the new price will be $14.

2 answers:

frozen [14]3 years ago

6 0

Answer: A,D,E

Step-by-step explanation:

Varvara68 [4.7K]3 years ago

5 0

The cost price of a swim-suit, C.P.=$8

Option 1:

If the selling price is marked up by 25%, the new selling price is

$S.P.=C.P.+C.P.\times 25\%$

$=8+8\times\frac{25}{100}$

=8+2

=10

So, the selling price will be $10 which is the same as the mentioned selling price.

Hence, this option is correct.

Option 2:

If the selling price is marked up by 40%, the new selling price is

$S.P.=C.P.+C.P.\times 40\%$

$=8+8\times\frac{40}{100}$

=8+3.20

=11.20

So, the selling price will be $11.20 which is not the same as the mentioned selling price, $7.50.

Hence, this option is wrong.

Option 3:

If the selling price is marked up by 55%, the new selling price is

$S.P.=C.P.+C.P.\times 55\%$

$=8+8\times\frac{55}{100}$

=8+4.40

=12.40

So, the selling price will be $12.40 which is not the same as the mentioned selling price, $5.50.

Hence, this option is wrong.

Option 4:

If the selling price is marked up by 70%, the new selling price is

$S.P.=C.P.+C.P.\times 70\%$

$=8+8\times\frac{70}{100}$

=8+5.60

=13.60

So, the selling price will be $13.60 which is the same as the mentioned selling price.

Hence, this option is correct.

Option 5:

If the selling price is marked up by 75%, the new selling price is

$S.P.=C.P.+C.P.\times 75\%$

$=8+8\times\frac{75}{100}$

=8+6

=14

So, the selling price will be $14 which is the same as the mentioned selling price.

Hence, this option is correct.

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21. Who is closer to Cameron? Explain.

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Problem 21

<h3>Answer: Jamie is closer</h3>

-----------------------

Explanation:

A = Arthur's location = (20,35)
J = Jamie's location = (45,20)
C = Cameron's location = (65,40)

To find out who's closer to Cameron, we need to compute the segment lengths AC and JC. Then we pick the smaller of the two lengths.

We use the distance formula to find each length

Let's find the length of AC.

$A = (x_1,y_1) = (20,35)\\\\C = (x_2,y_2) = (65,40)\\\\d = \text{Distance from A to C} = \text{length of segment AC}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(20-65)^2 + (35-40)^2}\\\\d = \sqrt{(-45)^2 + (-5)^2}\\\\d = \sqrt{2025 + 25}\\\\d = \sqrt{2050}\\\\d \approx 45.2769257\\\\$

The distance from Arthur to Cameron is roughly 45.2769257 units.

Let's repeat this process to find the length of segment JC

$J = (x_1,y_1) = (45,20)\\\\C = (x_2,y_2) = (65,40)\\\\d = \text{Distance from J to C} = \text{length of segment JC}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(45-65)^2 + (20-40)^2}\\\\d = \sqrt{(-20)^2 + (-20)^2}\\\\d = \sqrt{400 + 400}\\\\d = \sqrt{800}\\\\d \approx 28.2842712\\\\$

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We see that segment JC is shorter than AC. Therefore, Jamie is closer to Cameron.

=================================================

Problem 22

<h3>Answer: Arthur is closest to the ball</h3>

-----------------------

Explanation:

We have these key locations:

A = Arthur's location = (20,35)
J = Jamie's location = (45,20)
C = Cameron's location = (65,40)
B = location of the ball = (35,60)

We'll do the same thing as we did in the previous problem. This time we need to compute the following lengths:

AB
JB
CB

These segments represent the distances from a given player to the ball. Like before, the goal is to pick the smallest of these segments to find out who is the closest to the ball.

The steps are lengthy and more or less the same compared to the previous problem (just with different numbers of course). I'll show the steps on how to get the length of segment AB. I'll skip the other set of steps because there's only so much room allowed.

$A = (x_1,y_1) = (20,35)\\\\B = (x_2,y_2) = (35,60)\\\\d = \text{Distance from A to B} = \text{length of segment AB}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(20-35)^2 + (35-60)^2}\\\\d = \sqrt{(-15)^2 + (-25)^2}\\\\d = \sqrt{225 + 625}\\\\d = \sqrt{850}\\\\d \approx 29.1547595\\\\$

Segment AB is roughly 29.1547595 units.

If you repeated these steps, then you should get these other two approximate segment lengths:

JB = 41.2310563

CB = 36.0555128

-------------

So in summary, we have these approximate segment lengths

AB = 29.1547595
JB = 41.2310563
CB = 36.0555128

Segment AB is the smallest of the trio, which therefore means Arthur is closest to the ball.

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