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serious [3.7K]
2 years ago
14

Keith won a cash prize in an art competition. He gave his mother 2/5 of the money he won. Of the remainder, 1/4 was given to his

sister, and 2/3 was given to his brother. He had $15 left. How much was Keith’s cash prize?
please give me an explanation (I need it)
Mathematics
1 answer:
USPshnik [31]2 years ago
7 0

Answer:

300 dollars

Step-by-step explanation:

Let the original amount = x

x - 2/5x  was what his mother's share looked.

5/5 x - 2/5 x

3/5x is what is left.

3/5 x - 1/4 * 3/5 x - 2/3x * 3/5 = his sister's share and his brothers

3/5x - 1/4*3/5 x - 2/3 * 3/5 = 15

3/5x * (1 - 1/4 - 2/3) = 15

3/5 x 5/60 = 15

15 / 300 * x = 15

1/20  x = 15

x = 15 * 20

x = 300

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70% of days in june were sunny how many days were sunny
goblinko [34]

There are 30 days in June. So 30 days represent 100% of the days:

30 = 100%    &   x = 70%  

so 100x= 2100

x= 21  Days

I hope this helps you! =^-^=

6 0
3 years ago
A phone company offers two monthly plans. Plan A costs $23 plus an additional $0.12 for each minute of calls. Plan B costs $18 p
Alona [7]

Answer:

250 minutes of calling will cost same using both plans.

$53

Step-by-step explanation:

Please consider the complete question.

A phone company offers two monthly plans. Plan A costs $23 plus an additional $0.12 for each minute of calls. Plan B costs $18 plus an additional $0.14 of each minute of calls.  For what amount of calling do the two plans cost the same?  What is the cost when the two plans cost the same?

Let x represent the number of call minutes.

The total cost of calling for x minutes using plan A would be cost of x minutes plus fixed charge that is 0.12x+23.

The total cost of calling for x minutes using plan B would be cost of x minutes plus fixed charge that is 0.14x+18.

To find the number of minutes for which both plans will have same cost, we will equate total cost of x minutes for both plans and solve for x.

0.14x+18=0.12x+23

0.14x-0.12x+18=0.12x-0.12x+23

0.02x+18=23

0.02x+18-18=23-18

0.02x=5

\frac{0.02x}{0.02}=\frac{5}{0.02}

x=250

Therefore, calling for 250 minutes will cost same using both plans.

Upon substituting x=250 in expression 0.14x+18, we will get:

0.14(250)+18=35+18=53

Therefore, the cost will be $53, when the two plans cost the same.

5 0
2 years ago
The water from an outdoor fountain follows a path that is shaped like a parabola. The arch created by the water is 32 inches wid
exis [7]

Answer:

i dont understand

Step-by-step explanation:

oh wait... (0,0) (16,28) (0,33)

6 0
3 years ago
Solve the given linear Diophantine equation. Show all necessary work. A) 4x + 5y=17 B)6x+9y=12 C) 4x+10y=9
aliina [53]

Answer:

A) (-17+5k,17-4k)

B)  (-4+3k,4-2k)

C) No integer pairs.

Step-by-step explanation:

To do this, I'm going to use Euclidean's Algorithm.

4x+5y=17

5=4(1)+1

4=1(4)

So going backwards through those equations:

5-4(1)=1

-4(1)+5(1)=1

Multiply both sides by 17:

4(-17)+5(17)=17

So one integer pair satisfying 4x+5y=17 is (-17,17).

What is the slope for this equation?

Let's put it in slope-intercept form:

4x+5y=17

Subtract 4x on both sides:

     5y=-4x+17

Divide both sides by 5:

      y=(-4/5)x+(17/5)

The slope is down 4 and right 5.

So let's show more solutions other than (-17,17) by using the slope.

All integer pairs satisfying this equation is (-17+5k,17-4k).

Let's check:

4(-17+5k)+5(17-4k)

-68+20k+85-20k

-68+85

17

That was exactly what we wanted since we were looking for integer pairs that satisfy 4x+5y=17.

Onward to the next problem.

6x+9y=12

9=6(1)+3

6=3(2)

Now backwards through the equations:

9-6(1)=3

9(1)-6(1)=3

Multiply both sides by 4:

9(4)-6(4)=12

-6(4)+9(4)=12

6(-4)+9(4)=12

So one integer pair satisfying 6x+9y=12 is (-4,4).

Let's find the slope of 6x+9y=12.

6x+9y=12

Subtract 6x on both sides:

      9y=-6x+12

Divide both sides by 9:

       y=(-6/9)x+(12/9)

Reduce:

       y=(-2/3)x+(4/3)

The slope is down 2 right 3.

So all the integer pairs are (-4+3k,4-2k).

Let's check:

6(-4+3k)+9(4-2k)

-24+18k+36-18k

-24+36

12

That checks out since we wanted integer pairs that made 6x+9y=12.

Onward to the last problem.

4x+10y=9

10=4(2)+2

4=2(2)

So the gcd(4,10)=2 which means this one doesn't have any solutions because there is no integer k such that 2k=9.

6 0
3 years ago
I need answers ASAP! Thanks!
Daniel [21]

Step-by-step explanation:

43. P, U

44. 7

53. Airplanes can be traveling on different planes, one plane above the other. Cars on the same intersection are on the same plane.

55

a. You can choose (4 * 3 * 2)/(3 * 2) = 4 groups of 3 points in which order does not matter.

One of those combinations does not have K, so 3 combinations of the 4 have K.

p = 3/4

b. p = 1 since any three points are always coplanar.

3 0
3 years ago
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