Question

2. Составь математическую модель по словесной: сумма цифр двузначного числа равна 12, а разность числа единиц и числа десятков в этом числе в 12 раз меньше самого числа. Найди это число. Выбери все подходящие математические модели, обозначив цифру десятков t, а цифру единиц — b. 1 {t+b=12(b−t)⋅12=tb 2 {t+b=12b−t12=10t+b 3 {t+b=12(b−t)⋅12=10t+b 4 {t+b=12b−t=10t+b12 5 {t+b=12b−t=(10t+b)⋅12 6 {t+b=12b−t=tb12 Смотреть ответ mila110476 mila110476 Ответ: {t+b=12(b−t)⋅12=10t+b, или {t+b=12b−t=10t+b12 Объяснение: Само число можно записать в виде 10t+b, тогда, учитывая, что разность числа единиц и числа десятков в этом числе в 12 раз меньше самого числа, имеем второе уравнение: (b−t)⋅12=10t+b. 1 система правильная а вторая нет. Там надо написать t+b=12 b-t=(10t+b/12 это дробь). 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Answer 1

Давайте разберемся в этой задаче и составим правильные математические модели.

Пусть t обозначает цифру десятков, а b обозначает цифру единиц в двузначном числе. Тогда само число можно записать как 10t + b.

Условие задачи гласит, что сумма цифр двузначного числа равна 12:

1. t + b = 12

Также в условии сказано, что разность числа единиц и числа десятков в этом числе в 12 раз меньше самого числа:

2. b - t = (10t + b) / 12

Теперь давайте проверим каждую из предложенных математических моделей, чтобы определить правильную:

1. {t + b = 12, (b - t) * 12 = tb}
2. {t + b = 12, b - t = 12(10t + b)}
3. {t + b = 12, (b - t) * 12 = 10t + b}
4. {t + b = 12, b - t = 10t + b / 12}
5. {t + b = 12, b - t = (10t + b) * 12}
6. {t + b = 12, b - t = tb / 12}

Из этих моделей только 3 и 4 являются правильными.

• Модель 3: {t + b = 12, (b - t) * 12 = 10t + b}
• Модель 4: {t + b = 12, b - t = 10t + b / 12}

Обе этих модели правильные, так как они учитывают оба условия задачи. Вы можете выбрать любую из них для решения задачи.

Дополнительно замечу, что при использовании модели 4, вы должны быть внимательны при решении уравнения, так как есть дробь. Возможно, вы просто допустили небольшую ошибку при вычислениях.