Problem solving of Mathematics for Seventh Grade

Question 1

  A motorcycle needs 4 liters of gas for 144 km. How much gas is needed for 54 km?

Solution : 

First, we must find out how much gas needed for one kilometer.

The step for find it is divide 4 by 144.

      4/144=1/36

For one kilometer it needs 1/36  liters. To find how much gas that needed for 54 kilometer is multiply 54 with  1/36.

54 x 1/36 = 1.5 

Thus, a motorcycle needs 1.5 liters for 54 kilometer.

Question 2

A bamboo of 15 meters long is cut into two parts. The first part is 3 meters longer than the other. 

How long for each part of the bamboo?

Solution :

First, let the short part of bamboo is X. So the longer part is X+3 because it is 3 meters longer than the other one. We know that its length before cutted is 15. In other words

X+X+3=15

We can sum X and X so the it is become 2X.

2X+3=15

Then substract both sides with three.

2X+3-3=15-3

2X=12

Then divide both side with two.

2X : 2=12 : 2

X=6

So, we know that the value of X is 6.

Because of the length of short part bamboo is X we find that its length is 6.

In the first step we let the length of long part bamboo is X+3, then substitute X with 6.

6+3=9

So the length of long part bamboo is 9.

Finally we find that the length each part of bamboo after cutted are 6 meters and 9 meters.

Question 3 

Nyaman Hotel has 350 rooms. Sejuk Hotel has 450 rooms.  

Sejuk Hotel has 450 rooms.

The  3/7 of the total rooms in Nyaman Hotel have been reserved for holiday.

Determine the numbers of the rooms have been reserved in Sejuk Hotel for holiday if there are 400 rooms have been reserved in those two hotels.

Solution :

First, find out the reserved room in Nyaman Hotel by multiply 3/7 with sum of all rooms in Nyaman Hotel. That is 350 rooms.

  3/7 x 350= 150

From that operation we know that reserved room in Nyaman Hotel is 150 rooms.

The way to find how many reserved room in Nyaman Hotel is just substract 400 with 150.

400-150=250

So the number of reserved room in Nyaman Hotel is 250 rooms.

Question 4

Mr. Pandhu invested Rp 10,000,000.00 to the bank at 1.2 % interest per month. 

How much money due at the end of 5 years does Mr. Pandhu have?

Solution :

The first step to find how much his money due at the end of years is count interest that he gets at the end of 5 years. To find it just multiply the interest in a mounth with 5( number 5 in here means 5 years).

1.2% x 5 = 6%

The result is 6%. Then multiply again that result with 12 because there are 12 month in a year.

6% x 12 = 72%

So the interest rate after five years is 72%.

After that we count the interest represent in number(money) by multiply the interest rate after five years with the capital he has.

72% x 10,000,000=7,200,000

The interest in 5 years is 7,200,000.

To know how much his money in the bank is by sum the interest with the capital.

7,200,000+10,000,000=17,200,000

Hence, Mr. Pandhu’s money at the end of 5 years is Rp 17,200,000.00.

Question 5

  Find the following square roots of 289

Solution :

First, separate number 289 into two groups. That are 2 and 89.

2 | 89

Then look the number in the left group. That is 2. Find the number if it is squared the result will not more than 2.

The number is 1 because if 1 squared the result is not more than 2. After that, apply the substractional operation on the left group like this :

Add the result with that own number.

1+1=2

Move down the number in the right group. Place the number one under number 2

     

Keep the result to do the next calculating process. Then, fill in the ... with a number so that  if we multiply 2... with... the result is not more than 189 or same with 189. We use number 2 from the result of 1+1 that we have found before.

In this case, fill ... with 7 because if we multiply 27 with 7 the result is 189 (It’s not more than 189). Apply again the subtractional operation. The result of the subtractional is 0. So the process of finding the square root of 289 has finished. The result is 17.