At a technology fair, for every 4 phones there are 3 tablets

Question

At a technology fair, for every 4 phones there are 3 tablets. For every 2 tablets there are 5 kitchen robots. For every 4 kitchen robots there are 3 monitors. If there are 26 more monitors than phones, how many tablets are there?

(A) 36
(B) 48
(C) 60
(D) 64
(E) 72

Show Answer

Official Answer

B

(A) 36
(B) 48
(C) 60
(D) 64
(E) 72

Prakriti2600 · Answer

Phones to Tablets: For every 4 phones, there are 3 tablets.
 P = 4/3T 
Tablets to Kitchen Robots: For every 2 tablets, there are 5 kitchen robots
 K = 5/2T 
Kitchen Robots to Monitors: For every 4 kitchen robots, there are 3 monitors
 M =3/4K 
There are 26 more monitors than phones (M - P = 26). 
Substituting our expressions for M and P:
15/8T - 4/3T = 26
13T = 26 x 24
T = 2 x 24
 T = 48 (B)

kevincan · Answer

Also , M/P = M/R * R/T * T/P

hardikgaur99 · Answer

Didn't understand this. Can someone pls simplify this more?

raghavkohli31 · Answer

We can assume that there are 800 phones (just took a number to avoid decimals, we can take any number here)-
this means there are 3/4 * 800 = 600 tablets
for 600 tablets, there would be 600/2 * 5 = 1500 kitchen robots
for 1500 kitchen robots, there would be 1500/4 * 3 = 1125 monitors.

if there are 600 tablets, there are 1125-800 = 325 more monitors than phones,
for how many tablets would there be 26 more monitors than phones.

600/325 * 26 = 48.

kevincan · Answer

When you read there are 4 phones for every three tablets , you can represent this relationship between P the number of phones and T the number of tablets in several ways :

P:T = 4:3

\frac{P}{T}=\frac{4}{3}

\frac{T}{P}=\frac{3}{4}

3P = 4T

P = \frac{4}{3}T

T = \frac{3}{4}P

\frac{P}{P+T}=\frac{4}{7}

\frac{T}{P+T}=\frac{3}{7}

P = 4k,\quad T = 3k

This last one is often my favorite!

kevincan · Answer

A very fast approach is to go directly from phones to monitors:

\frac{T}{P}=\frac34,\quad

\frac{K}{T}=\frac52,\quad

\frac{M}{K}=\frac34

so

\frac{M}{P}= \frac34\cdot\frac52\cdot\frac34=\frac{45}{32}.

Then  M=45k , P=32k, . We are told that the difference between the number of monitors and the number of tablets is 26. Therefore,  13k = 26  so  k= 2  and  T =48.

egmat · Answer

Hi hardikgaur99,

The solution Prakriti posted is correct, but the fractions make it hard to see what's going on. Let's redo it with  whole numbers only , no fractions.

The trick is to write all four items in  one single ratio , scaling so the shared item matches each time.

Step 1 - line up phones, tablets, robots. 
- Phones : Tablets =  4 : 3 
- Tablets : Robots =  2 : 5

To join them, make the tablets match. Tablets is  3  in the first and  2  in the second, so scale both to  6 :
- Phones : Tablets =  8 : 6 
- Tablets : Robots =  6 : 15

Now they share tablets =  6 , so:  Phones : Tablets : Robots = 8 : 6 : 15

Step 2 - bring in monitors. 
- Robots : Monitors =  4 : 3

Robots is  15  above and  4  here, so scale to a common  60 :
- Phones : Tablets : Robots =  32 : 24 : 60  (multiplied by  4 )
- Robots : Monitors =  60 : 45  (multiplied by  15 )

Putting it all together:

Phones : Tablets : Robots : Monitors = 32 : 24 : 60 : 45

Step 3 - use the "26 more monitors than phones" clue.

In ratio units, Monitors - Phones =  45 - 32 = 13  units. The problem says that gap is  26  actual items, so:

-  13  units =  26  -  1  unit =  2

Tablets are  24  units, so:

- Tablets =  24  x  2  =  48

That's answer  B .

The whole idea: instead of juggling fractions, turn the chain of ratios into one clean string of whole numbers, then let the " 26  more" clue tell you what one unit is worth.

Answer: B

At a technology fair, for every 4 phones there are 3 tablets

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