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zlopas [31]
3 years ago
7

A teacher has two students, one two times as old as the other. The teacher is five times as old as the older student, and in 5 y

ears she will be five times as old as her younger student. Find the teacher’s present age.
Mathematics
2 answers:
yuradex [85]3 years ago
8 0

Answer:

40 years

Step-by-step explanation:

kramer3 years ago
6 0
Let's call the younger student's age A and the older student's age B. The teacher's age will be T.

B = 2A
T = 5B
T+5 = 5(A+5)

Simplify the last equation.

T+5 = 5A+25
T = 5A+20

Now we have two equations solved for T, so we can set them equal to each other.

5B = 5A + 20

We can plug 2A in for B

5(2A) = 5A + 20

10A = 5A + 20

5A = 20

A = 4

To find T, we plug 4 in for A in T = 5A + 20

T = 5(4) + 20

T = 40

The answer is 40 years old.


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A box is partially filled with books. If 24 cubic inches of the box are already filled and there are 12 cubic inches of space le
nikitadnepr [17]

Answer:

The box has a total volume of 36 cubic inches.

Step-by-step explanation:

The total volume of the box is given by the volume that is filled with books plus the volume that doesn't have any books in it. Therefore, in order to solve this problem we must sum the two volumes. We have:

total volume = volume with books + volume without books

total volume = 24 + 12

total volume = 36 cubic inches

The box has a total volume of 36 cubic inches.

4 0
3 years ago
Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost $228. Write and solve a s
Temka [501]
22a+15c=228
a+c=11

a=11-c

22(11-c) + 15c = 228

242-22c + 15c = 228

-7c=-14

C = 2 (two children)

Remember how a + c = 11

a + 2 = 11

A= 9

9 adults, 2 children.
5 0
4 years ago
Explain how to find the value of x. Be sure to include the postulates, definitions and theorems that justify your answer.
Black_prince [1.1K]

Answer: x = 12

Step-by-step explanation:

We can see two triangles rectangles, we will use the angle S to solve this, as this angle is common to both triangles.

We know that:

cos(S) = adj cathetus/hipotenuse.

Then we have, for the triangle SRT.

Cos(S) = 9/SR.

for the big triangle, SQR, we have:

Cos(S) = SR/(9 + 16)

now we can find the quotient of those two equations and get:

cos(S)/cos(S) = 9/Sr*(9+16)/SR

SR^2 = 9*(25)

SR =  15.

Now with this side we can find the value of x.

We can use the Pythagorean theorem in the triangle SRT, where the sum of the squared cathetus is equal to the hypotenuse:

9^2 + x^2 = 15^2

x = √(15^2  - 9^2) = 12

7 0
3 years ago
There is a bag filled with 3 blue and 4 red marbles.
Tasya [4]

Answer:

here

Step-by-step explanation:

The probability of getting 1 red is 4/7. The probability of getting 2 reds in a row is (4/7)^2 = 16/49.

4 0
3 years ago
Buddy painted (1/5) of the 320 nutcrackers.How many nutcrackers did buddy paint
just olya [345]

Answer:

64

Step-by-step explanation:

Given that,

Buddy painted (1/5) of the 320 nutcrackers.

We need to find how many nutcrackers did buddy paint. It can be calculated by finding (1/5) of 320.

x=\dfrac{1}{5}\times 320\\\\=64

Hence, he painted 64 nutcrackers.

3 0
3 years ago
Read 2 more answers
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