# Direct Variations Using Method of Proportion

Now we will learn how to solve direct variations using method of proportion.

We know, the two quantities may be linked in such a way that if one increases, other also increases. If one decreases, the other also decreases.

Some situations of direct variations:

● More articles, more money required to purchase.

● More men at work, more work will be done.

● More speed, more distance covered in fixed time.

● More money borrowed, more interest to be paid.

● More working hours, more work will be done.

Solved examples on direct variations using method of proportion:

1. The cost of 5 kg of rice is $30. What will the cost of 12 kg of sugar be? Solution: This is a situation of direct variation, now we solve using method of proportion. More quantity of rice results in more cost. Here, the two quantities vary directly (Quantity of rice and cost of rice)  Weight of rice (kg) 5 12 Cost 30 x Since, they vary directly Therefore, 5/30 = 12/x (cross multiply) ⇒ 5x = 30 × 12 ⇒ x = (30 × 12)/5 = 72 Therefore, cost of 12 kg rice =$ 72

2. If 9 drawing books cost 171, what do 22 books cost?

Solution:

This is a situation of direct variation, now we solve using method of proportion.

More number of drawing books results in more cost.

Here, the two quantities vary directly (Number of drawing books and cost of drawing books)

 Number of drawing books 9 22 Cost 171 x

Since, they vary directly

Therefore, 9/171 = 22/x    (cross multiply)

⇒ 9x = 171 × 22

⇒ x = (171 × 22)/9 = 418

Therefore, cost of 22 drawing books = $418 3. A worker gets$ 504 for 7 days of work. How many days should he work to get $792? Solution: This is a situation of direct variation, now we solve using method of proportion. More money, more days of work Here, the two quantities vary directly. (Amount and days of work)  Number of working days 7 x Amount Obtained ($) 504 792

Since, they vary directly

Therefore, 7/504 = x/792

⇒ 504x = 792 × 7

⇒ x = (792 × 7)/504

Therefore, 792 earned by the workers in = 11 days

Problems Using Unitary Method

Situations of Direct Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation