please need help don't know

Question

I tried and i tried and still can't get the right answer.

A scale on a map shows that 2 inches = 25 miles.

Part A
How many inches on the map represent 60 miles?

Part B
How many miles are represented by 1/4 inch on the map?

Answer 1

Nathan B. points out that this is a RATIO problem (each type of algebra problem is solved using the same method, regardless of the values of the variables).  I’m just mentioning some ideas so you won’t have to “try and try and still not get the right answer.”

A ration is a fraction.  In word problems, look for words like “per” and “in” or “scale.”  It is extremely important that you keep the units straight, so it’s o.k. to write them throughout your solution.

The scale, or ratio, is given as     (2 inches) / (25 miles).

If you use I for map inches and M for land miles, this is

      I / M  = 2/25  inches/mile

Now, either solve for I = (2/25) * M   inches/mile

   Or for  M = I / (2/25)   miles/inch    =   (25*I / 2) miles/inch

So, you can easily find either I given M or else M given I.

Part A.  Given M=60 miles on land find I inches on the map.

Part B.  Given I = 1/4 inches on the map find M miles on land.

I’m not sure why Nathan B. showed one result as a fraction and the other as a decimal (your teacher or the problem probably prefers one or the other).  So,

    4 4/5  =  4.8

And

    3.125  =  3 1/8

 

Answer 2

Hi Conner!  

 

For this problem, think about proportions.  I'm going to use slightly different numbers as an example.

 

A scale on a map shows that 3 inches = 20 miles.

Part A
How many inches on the map represent 85 miles?

 

By using proportions, see that 3 is to 20 as x is to 85.  You can set this up as: 3/20 = x/85.

Solving for x, we get:  (3*85)/20 = x.  Simplifying, we see that x = 12.75.  

So 12.75 inches represent 85 miles.  

Part B
How many miles are represented by 1/5 inch on the map?

 

Again we use proportions.  See that 1/5 is to x as 3 is to 20.  Set this up as: (1/5)/x = 3/20.

Cross multiply to get (1/5)*20 = 3x.  Simplifying gives 4 = 3x, and thus x = 4/3.  

So 4/3 miles are represented by 1/5 inch on the map.

 

 

Do this examples make sense and help?  If so, try doing your problem again on your own.  If you get stuck, let me know and I'll help with the actual problem.  If not, feel free to ask questions on the example I gave!

Answer 3

Part A:

Let's try turning this into a ratio problem:

^{2 in}/_{25 mi} = ^x/_{60 mi}

 

We need to isolate x, so we multiply both sides by 60 mi:

^{2 in * 60 mi}/_{25 mi} = x

We can simplify a little:

^{2 in* 12}/₅ = x

^{24 in}/₅ = x

4 ⁴/₅ in = x

 

Part B

If 2 in = 25 mi, then 1 in = 12.5 mi

12.5 mi/ 4 = 3.125 mi