QuestionІЭгшитгэл зохиож бод:
Энхжин өглөө, өдөр, орой гэсэн гурван удаа өрөөнийхөө дулааныг хэмжихэд өглөө 19 хэм, өдөр оройноос 7 хэмээр дулаан байсан ба тэдгээрийг нэмэхэд 62 гарав. Эндээс орой хэдэн хэм дулаан байсныг ол.

Studdy Solution

STEP 1

Assumptions
1. Let $T_{\text{morning}}$ be the temperature in the morning.
2. Let $T_{\text{afternoon}}$ be the temperature in the afternoon.
3. Let $T_{\text{evening}}$ be the temperature in the evening.
4. The morning temperature $T_{\text{morning}} = 19$ degrees.
5. The afternoon temperature is 7 degrees warmer than the evening temperature.
6. The sum of the morning, afternoon, and evening temperatures is 62 degrees.

STEP 2

Express the afternoon temperature in terms of the evening temperature.
Given that the afternoon temperature is 7 degrees warmer than the evening temperature, we can write:
$T_{\text{afternoon}} = T_{\text{evening}} + 7$

STEP 3

Set up the equation for the sum of the temperatures.
According to the problem, the sum of the morning, afternoon, and evening temperatures is 62 degrees:
$T_{\text{morning}} + T_{\text{afternoon}} + T_{\text{evening}} = 62$

STEP 4

Substitute the known values and expressions into the equation.
Substitute $T_{\text{morning}} = 19$ and $T_{\text{afternoon}} = T_{\text{evening}} + 7$ into the equation:
$19 + (T_{\text{evening}} + 7) + T_{\text{evening}} = 62$

STEP 5

Simplify the equation.
Combine like terms:
$19 + T_{\text{evening}} + 7 + T_{\text{evening}} = 62$
$26 + 2T_{\text{evening}} = 62$

STEP 6

Solve for the evening temperature $T_{\text{evening}}$ .
Subtract 26 from both sides:
$2T_{\text{evening}} = 62 - 26$
$2T_{\text{evening}} = 36$
Divide both sides by 2:
$T_{\text{evening}} = \frac{36}{2}$
$T_{\text{evening}} = 18$
The evening temperature was 18 degrees.

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