Question

A sum of $2700 is to be given in the form of 63 prizes. If the prize is of either $100 or $25, find the number of prizes of each type.

I'll give 40 point for a detail explanation please:)​

Answer 1

Ответ:

 15 prizes of $100 and 48 prizes of $25

Пошаговое объяснение:

Let the number of $100 prizes be x and the number of $25 prizes be y. Then we have two equations:

x + y = 63 (total prizes are 63) 100x + 25y = 2700 (total prizes are $2700)

We can solve for x and y using substitution or elimination. Here we will use replacement.

From the first equation, we have y = 63 - x. Substituting this into the second equation, we get:

100x + 25(63 - x) = 2700

Simplifying and solving for x, we get:

75x + 1575 = 2700

75x = 1125

x = 15

So there are 15 prizes of $100 each. Substituting this back into the equation y = 63 - x, we get:

y = 63 - 15

y = 48

So there are 48 prizes of $25 each.

So there are 15 prizes of $100 and 48 prizes of $25.

Answer 2

$100 prizes be x and the number of $25 prizes be y.

total number of prizes is 63, so:

x + y = 63

total amount of money in prizes is $2700, so:

100x + 25y = 2700

We can use the first equation to solve for x in terms of y:

x = 63 - y

substitute this expression for x in the second equation:

100(63 - y) + 25y = 2700

Expanding and simplifying:

6300 - 100y + 25y = 2700

-75y = -3600

y = 48

So there are 48 prizes of $25.

substitute this value for y in the equation x + y = 63 to find x:

x + 48 = 63

x = 15

So there are 15 prizes of $100.

there are 15 prizes of $100 and 48 prizes of $25.