Question

A man has 27 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 495 cents, how many dimes and how many quarters does he have? Если можно дайте ответ с коротким объяснением Спасибо!!!!!!!

Answer 1

Ответ: 12 dimes and 15 quarters

Пошаговое объяснение: dime = 10 cents, quarter = 25 cents; пусть d - количество dimes, а q - количество quarters; составляем уравнения:

(1) d + q = 27

(2) 10 * d + 25 * q = 495

Умножаем (1) на -10 и складываем со (2):

-10d - 10q + 10d + 25q = -270+495,

15q = 225

q = 15

d = 27 - q = 12

Answer 2

Let's assume the man has x dimes and y quarters. Since he has a total of 27 coins, we can write the equation:

x + y = 27 (Equation 1)

The value of x dimes is 10x cents, and the value of y quarters is 25y cents. The total value of his change is given as 495 cents, so we can write another equation:

10x + 25y = 495 (Equation 2)

Now, we have a system of equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.

By rearranging Equation 1, we get:

x = 27 - y

Substituting this value of x into Equation 2, we get:

10(27 - y) + 25y = 495 270 - 10y + 25y = 495 270 + 15y = 495 15y = 495 - 270 15y = 225 y = 225/15 y = 15

Substituting this value of y back into Equation 1, we get:

x + 15 = 27 x = 27 - 15 x = 12

Therefore, the man has 12 dimes and 15 quarters.