Given that 14t = 2d, 5p = 2c, 4c = 9m, and 12p = 63t, what is 15d in the units of m? (Assume all the numbers in equalities as exact numbers.)

Question

Create an image of a chalkboard displaying four mathematical equations. The first equation has two variables, t and d, and it reads '14t = 2d'. The second equation has two variables, p and c, and it reads '5p = 2c'. In the third equation, the variables c and m are present, which reads '4c = 9m'. For the fourth expression, the variables are p and t and the equation is '12p = 63t'. There should be no text apart from these four equations. Styled in a classroom setting without any identifiable characters or objects.

Given that 14t = 2d, 5p = 2c, 4c = 9m, and 12p = 63t, what is 15d in the units of m? (Assume all the numbers in equalities as exact numbers.)

Answer 1

15/2 * (14t = 2d) ... 105t = 15d

15d = 105t * (12p / 63t) * (2c / 5p) * (9m / 4c)

Answer 2

Well, if we rearrange the first equation 14t = 2d, we can isolate d: d = 14t/2. And since 12p = 63t, we can rewrite it as p = 63t/12.

Now, substituting these values into the second equation: 5p = 2c becomes 5(63t/12) = 2c.

Simplifying that, we get 15.75t = 2c.

And since 4c = 9m, we can rewrite it as c = 9m/4.

Substituting this into our previous equation: 15.75t = 2(9m/4).

Simplifying further, we have 31.5t = 9m.

Finally, with a little bit of rearranging, we find that 15d = 31.5t. So, if we replace t with d, we get 15d = 31.5d.

Therefore, 15d in the units of m is equal to 31.5d.

Answer 3

To find the value of 15d in the units of m, we need to first determine the values of t, p, and c in terms of m.

Let's start by using the first equation, 14t = 2d. We can isolate t by dividing both sides of the equation by 14:

14t/14 = 2d/14

t = (2/14)d

Next, let's use the fourth equation, 12p = 63t. Substituting the value we found for t:

12p = 63(2/14)d

Simplifying:

12p = (9/2)d

We can isolate p by dividing both sides of the equation by 12:

12p/12 = (9/2)d/12

p = (3/8)d

Now, let's use the second equation, 5p = 2c. Substituting the value we found for p:

5(3/8)d = 2c

Simplifying:

(15/8)d = 2c

We can isolate c by dividing both sides of the equation by 2:

(15/8)d/2 = c

c = (15/16)d

Finally, let's use the third equation, 4c = 9m. Substituting the value we found for c:

4(15/16)d = 9m

Simplifying:

(60/16)d = 9m

Reducing the fraction:

(15/4)d = 9m

Now, to find the value of 15d in the units of m, we can rearrange the equation:

15d = (4/15)(9m)

Simplifying:

15d = (36/15)m

Dividing both sides of the equation by 15:

d = (36/15)(1/15)m

Now we can substitute the value of d into the equation:

15d = (36/15)m

15(36/15)(1/15)m = 15(36/15)m

Using the commutative property of multiplication:

15(36/225)m = 15(36/15)m

Finally, simplifying:

15(2/5)m = 6m

Therefore, 15d is equal to 6m in the given equations.

Answer 4

To find the value of 15d in the units of m, we need to manipulate the given equations to isolate the variable d. Let's start by solving for t in terms of d using the equation 14t = 2d.

Divide both sides of the equation by 14:
14t/14 = 2d/14
t = d/7

We now have an expression for t in terms of d. Next, let's substitute this value of t into the equation 12p = 63t to find p in terms of d.

Substitute t = d/7 into the equation:
12p = 63(d/7)

Simplify the equation:
12p = 9d

Now, we have an expression for p in terms of d. Let's proceed to substitute this value of p into the equation 5p = 2c to find c in terms of d.

Substitute p = 9d/12 into the equation:
5(9d/12) = 2c

Simplify the equation:
15d/4 = 2c

Finally, we have an expression for c in terms of d. Moving on, let's substitute this value of c into the equation 4c = 9m to find m in terms of d.

Substitute c = (15d/4) into the equation:
4(15d/4) = 9m

Simplify the equation:
15d = 9m

Now we have an equation relating d and m. Rearrange the equation to solve for m:
9m = 15d

Divide both sides of the equation by 9:
9m/9 = 15d/9
m = 5d/3

So, we have found that 15d in the units of m is equal to (5d/3).