Math  /  Algebra

QuestionТом, жижиг ачааны машины даац нийлээд 14 тонн. Хэрэв 22 жижиг машинд 10 том машинаас 20 тонн илүү ачаа ачих бол жижиг машины даац хэд вэ?

Studdy Solution

STEP 1

Assumptions
1. The load capacity of one large truck is TT tons.
2. The load capacity of one small truck is SS tons.
3. The combined load capacity of one large truck and one small truck is 14 tons.
4. 22 small trucks carry 20 tons more than 10 large trucks.

STEP 2

Express the relationship between the load capacities of the large and small trucks.
T+S=14 T + S = 14

STEP 3

Express the total load carried by 10 large trucks.
10T 10T

STEP 4

Express the total load carried by 22 small trucks.
22S 22S

STEP 5

According to the problem, 22 small trucks carry 20 tons more than 10 large trucks.
22S=10T+20 22S = 10T + 20

STEP 6

We now have a system of two equations:
1. T+S=14T + S = 14
2. 22S=10T+2022S = 10T + 20

STEP 7

Solve the first equation for TT.
T=14S T = 14 - S

STEP 8

Substitute T=14ST = 14 - S into the second equation.
22S=10(14S)+20 22S = 10(14 - S) + 20

STEP 9

Expand the equation.
22S=14010S+20 22S = 140 - 10S + 20

STEP 10

Combine like terms.
22S=16010S 22S = 160 - 10S

STEP 11

Add 10S10S to both sides to isolate terms involving SS.
22S+10S=160 22S + 10S = 160

STEP 12

Combine the SS terms.
32S=160 32S = 160

STEP 13

Solve for SS by dividing both sides by 32.
S=16032 S = \frac{160}{32}

STEP 14

Calculate the value of SS.
S=5 S = 5
The load capacity of a small truck is 5 tons.

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