If someone can answer this math problem this would mean alot to me because my math tutor couldnt even figure?

Question

this out. Here's the problem. - A reservation clerk worked 14.4 hours one day. She spent twice as much time entering new reservations as she did verifying old ones and one and a half as much time calling to confirm reservations as verifying old ones. How much time did she spend entering new reservations. (If anyone can work this problem out and show me how u did it, it would be very appreciated. thanks.) the answer is 6.4 hours but I saw that on the back of the answer key of the study guide, but me and my tutor can't come out with the same answer.

Answer 1

Fortunately there is a step by step way to do this.

1. Assign variables to all your unknowns. Here these are N (enter news reservations), V (verifying old ones) and C (confirming reservations)

2. For each statement, write an equation:

Assuming that all 14.4 hours is taken by the three activities:

N + V + C = 14.4

The first half of the second sentence says: N = 2 V

The second half says: C = (3/2) * V

3. Solve your equations, usually by substitution. You want to find N. You have three equations:

a) N + V + C = 14.4
b) N = 2 V
c) C = (3/2) * V

Since you want to find N, you need figure out what V and C are ion terms of N. Equation b says:

V = N/2

Combining b and c:

C = (3/2)V = (3/2)(N/2) = (3/4)N

Substitute these into a:

N + V + C = 14.4
N + N/2 + (3/4)N = 14.4
N * (9/4) = 14.4
N = 14.4*4/9 = 6.4 hrs.

Answer 2

A) Old + New + Confirming = 14.4

B) 2 * Old = New

C) Confirming = 3/2 * Old

Replace New in A with B:

Old + 2 * Old + Confirming = 14.4

Replace Confirming using C:


Old + 2 * Old + 3/2 * Old = 14.4

9/2 * Old = 14.4


Multiply both sides by 2/9:

Old = 14.4 * 2 / 9 = 3.2

Substitute into B:

2 * Old = New

New = 6.4

Answer 3

time entering new reservations = N

time verifying old ones = O

time calling to confirm reservations = C

From the question

N = 2 O
C = 1.5 O

Total time =14.4 = N + C + O

substitute from above for N and C gives

14.4 = 2 O + 1.5 O + O = 4.5 O

so O = 14.4/4.5 =3.2

But from above N = 2 O

so N= 6.4

Answer 4

First, let x be the number of hours spent verifying old reservations.
Then 2x is the amount of time spent entering new reservations and 1.5x is the amount of time spent calling to confirm reservations.

Since the total time worked was 14.4 hours,
x + 2x + 1.5x = 14.4
4.5x = 14.4
x = 14.4/4.5
x = 3.2

So, 3.2 hours was spent on verifying old reservations,
2(3.2) = 6.4 hours were spent on entering new reservations,
and 1.5(3.2) = 4.8 hours were spent on calling to confirm reservations.

Answer 5

Let
t = verifying old reservations
2t = time entering new reservations
1.5t = confirming reservations

t + 2t + 1.5t = 14.4
4.5t = 14.4
t = 14.4/4.5 = 144/45 = 16/5

2t = 2(16/5) = 32/5 = 6.4 hours

Answer 6

E = entering new reservations

V = verifying old reservations

C = confirming reservations

E = 2V

C = 1.5V

E + V + C = 14.4

2V + V + 1.5V = 14.4

V = 14.4/(2 + 1 + 1.5) = 14.4/4.5 = 3.2 hrs

E = 2V = 2*3.2 = 6.4 hrs

Answer 7

Let x be the time taken for verifying old records.

Time taken for entering new reservations = 2x
Time taken for calling reservations = 1.5x

Hence,
2x + 1.5x + x = 14.4
4.5x = 14.4
x = 3.2

=> Time taken for entering new reservations = 2(3.2) = 6.4