1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Slav-nsk [51]
3 years ago
11

Simon and Greg shared pencils in the ratio 7:5. If Simon gives away 30 pencils and Greg gets 30 more pencils, they will have the

same number of pencils. How many did each of them have in the beginning?
Mathematics
1 answer:
Nutka1998 [239]3 years ago
8 0
7/5=s/g multiply both sides by g

7g/5=s  multiply both sides by 5/7

g=5s/7

We are then told that:

g+30=s-30  subtract 30 from both sides

g=s-60, and from earlier g=5s/7, and g=g so we can say:

s-60=5s/7  multiply both sides by 7

7s-420=5s  subtract 5s from both sides

2s-420=0  add 420 to both sides

2s=420 divide both sides by 2

s=210, and since g=s-60

g=150

So Simon had 210 pencils and Greg had 150 pencils.

Check..

s:g=210:150=7:5

and

s-30=g+30

210-30=150+30

180=180
You might be interested in
An apartment building produces $4,000 per quarter in gross rents. The maintenance expenses run $350 per month. Property taxes ar
erica [24]

Answer:

0.16%

Step-by-step explanation:

Cost of rent per quarter = $4000

Cost of rent per year = 4×$4000

= $16,000

This means that the apartment building produces $12,000 per year in gross rents.

Yearly Expenses are as follows;

Maintenance expenses per year = 12×$350 = $4200

Property taxes per year = $1,750

Mortgage payment per year = 12×$650 = $7800

Total expenses per year = sum of all the yearly expenses

= $4200+$1,750+$7800

= $13750

Yearly revenue generated = Cost of rent per year - total yearly expenses

= $16,000-$13750

= $2250 (net operating income)

Capitalization rate is given as the ratio of the net operating income to the market value of the building.

Capitalization rate = net operating income/market value of building

Since the building with $83750, that will be its market value

Cap rate = $13750/$83750

Cap rate = 0.16%

6 0
3 years ago
PLEASE HELP me with the magic square
defon

Fill in each slot in the square with variables <em>a</em>, <em>b</em>, <em>c</em>, <em>d</em>, and <em>e</em>, in order from left-to-right, top-to-bottom. In a magic square, the sums across rows, columns, and diagonals all add up to the same number called the <em>magic sum</em>.

The magic sum is -3.9, since "diagonal 2" (bottom left to top right) has all the information we need:

3 + (-1.3) + (-5.6) = -3.9

Use this to find the remaining elements

  • row 1:

<em>a</em> + <em>b</em> + (-5.6) = -3.9

  • row 2:

<em>c</em> + (-1.3) + <em>d</em> = -3.9

  • row 3:

3 + <em>e</em> + 0.02 = -3.9

  • column 1:

<em>a</em> + <em>c</em> + 3 = -3.9

  • column 2:

<em>b</em> + (-1.3) + <em>e</em> = -3.9

  • column 3:

(-5.6) + <em>d</em> + 0.02 = -3.9

  • diagonal 1 (top left to bottom right):

<em>a</em> + (-1.3) + 0.02 = -3.9

You will find

<em>a</em> = -2.62

<em>b</em> = 4.32

<em>c</em> = -4.28

<em>d</em> = 1.68

<em>e</em> = -6.92

5 0
2 years ago
What is the area of this composite figure?
Gelneren [198K]

Answer:

249 centimeters squared

Step-by-step Explanation:

The area of the rectangle: l x w, where l is the length and w is the width.

= 15.5 x 18

= 279

Area of the smaller rectangle: l x w, where l is the length and w is the width.

= 4 x 7.5

= 30

We do not need this 30.

Area of the shaded region:

= 279 - 30

= 249 cm²

5 0
2 years ago
a line is perpendicular to y - 5 = -1/4(x + 8) and goes through the point (-1,2). What is the lines y-intercept?
lisabon 2012 [21]

Answer:

y = 4x + 6

Step-by-step explanation:

Turn the equation we are given into slope-intercept form.

y - 5 = -1/4(x + 8)

y - 5 = -1/4x - 2

y = -1/4x + 3

The slope of a perpendicular line is the opposite reciprocal of the original line.

-1/4 -> 4/1 -> 4

Find the new y-intercept using the point given.

y = 4x + b

2 = 4(-1) + b

2 = -4 + b

6 = b

Fill in everything we solved for.

y = 4x + 6

Best of Luck!

8 0
3 years ago
Determine whether the system of equations has no solution, one solution, or infinitely many solutions
Vinil7 [7]

Answer:

one solution

Step-by-step explanation:

y=-3x+5

y=1/2x-2

You can tell straight off the bat, it does have a solution, and it isn't infinite solutions. If it had no solution, it would have the same slope but different y-intercepts. If it had infinite solutions, the 2 equations would have to be the exact same. So there is only one solution.

---

hope it helps

4 0
3 years ago
Other questions:
  • 12ad^3 and which terms are like terms?<br> 15a^3d<br> 12d^3<br> 3ad^3<br> 10ad
    13·1 answer
  • How to find a matrix that transform a column matrix from linear to circular quantum mechanic?
    15·1 answer
  • The perimeter of the base of the prism is __ units.
    15·1 answer
  • If x+1÷x=5 then x^19+1÷x^19=?​
    11·1 answer
  • Taylor wants to buy a bicycle that costs $48.75. She works for her mom after school to earn the money. If Taylor is paid $4.50 p
    12·2 answers
  • What is the sum of the series? Write in expanded form making sure to show all steps used to find the sum.
    13·1 answer
  • 6. Meg measured the length of some pieces
    15·1 answer
  • -25-6= -25 + -6 = -31
    5·1 answer
  • Help me solve this... i have a time limit so answer fast!!!
    9·2 answers
  • What contribution to geometry is attributed to the work of rene descartes
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!