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
svetoff [14.1K]
3 years ago
13

Keiko, Chang, and Abdul sent a total of 109 text messages over their cell phones during the weekend. Keiko sent 7 fewer messages

than Chang. Abdul sent 4
times as many messages as Keiko. How many messages did they each send?
Mathematics
1 answer:
lbvjy [14]3 years ago
5 0

9514 1404 393

Answer:

  • Keiko: 17
  • Chang: 24
  • Abdul: 68

Step-by-step explanation:

Let c represent the number of messages sent by Chang. Then Keiko sent (c-7) messages, and Abdul sent 4(c-7) messages. The total number sent was ...

  c + (c -7) +4(c -7) = 109

  6c -35 = 109 . . . . . . . . . . simplify

  6c = 144 . . . . . . . . . . . add 35

  c = 24 . . . . . . . . . . . divide by 6

  c-7 = 17

  4(c-7) = 68

Keiko sent 17, Chang sent 24, and Abdul sent 68 text messages.

You might be interested in
Which point represents the opposite of -2?
nataly862011 [7]

Answer:

2

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Solve the differential equation (2x+y)dx+(x−2y)dy = 0
ruslelena [56]

Answer:

y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))

Step-by-step explanation:

Solve 2 x + y(x) + (dy(x))/(dx) (x - 2 y(x)) = 0:

Let P(x, y) = 2 x + y and Q(x, y) = x - 2 y.

This is an exact equation, because (dP(x, y))/(dy) = 1 = (dQ(x, y))/(dx).

Define f(x, y) such that (df(x, y))/(dx) = P(x, y) and (df(x, y))/(dy) = Q(x, y).

Then, the solution will be given by f(x, y) = c_1, where c_1 is an arbitrary constant.

Integrate (df(x, y))/(dx) with respect to x in order to find f(x, y):

f(x, y) = integral(2 x + y) dx = x^2 + x y + g(y) where g(y) is an arbitrary function of y.

Differentiate f(x, y) with respect to y in order to find g(y):

(df(x, y))/(dy) = d/(dy) (x^2 + y x + g(y)) = x + (dg(y))/(dy)

Substitute into (df(x, y))/(dy) = Q(x, y):

x + (dg(y))/(dy) = x - 2 y

Solve for (dg(y))/(dy):

(dg(y))/(dy) = -2 y

Integrate (dg(y))/(dy) with respect to y:

g(y) = integral-2 y dy = -y^2

Substitute g(y) into f(x, y):

f(x, y) = x^2 - y^2 + y x

The solution is f(x, y) = c_1:

x^2 - y^2 + y x = c_1

Solve for y:

y(x) = 1/2 (x - sqrt(5 x^2 - 4 c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 - 4 c_1))

Simplify the arbitrary constants:

Answer:  y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))

5 0
2 years ago
Express 11 out of 25 as a percentage
Alexeev081 [22]

Answer:

44%

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Simplify.
Ket [755]
First off, nicely done on the exponents. You'd be surprised on how bad some look ,:D

a)
(3xy^{3})(2x^{2}y)\\ (3*2)(x*x^{2})(y^{3}*y)\\\\ 6x^{3}y^{4}

b)
2y(2y+3y^{2})-y^{2}(3-y)\\ (4y^{2}+6y^{3}) + (-3y^{2}+y^{3})\\ (6y^{3}+y^{3})+(4y^{2}-3y^{2})\\ 7y^{3}+y^{2}\\\\ y^{2}(7y+1)
8 0
3 years ago
There are 80 red balloons and 20 green balloons each package of balloons. What is the unit rate in red balloons per green balloo
I am Lyosha [343]
4 is the answer because for every green balloon there are 4 red balloons
5 0
3 years ago
Read 2 more answers
Other questions:
  • helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
    6·2 answers
  • What is 2/9 divided by 9/8
    8·2 answers
  • Need help please help me
    12·1 answer
  • Y is equal to x plus 6 A y=x-6 B y=x+6 C y=x+6 D x=y+6
    6·1 answer
  • Convert the following percent into common fractions in simplest form: 5 1/3%​
    14·1 answer
  • Which of the following is equal to the square root of the cube root of 2?
    7·1 answer
  • If 60 percent of h is 80, what is 30 percent of h?
    15·2 answers
  • -5(4-n)=1+2n<br> Anyone know this
    11·1 answer
  • (b) A farmer uses of his land to plant
    14·1 answer
  • Prove the LL theorem for right triangles
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!