Question

A deck of cards has 12 cards that are Kings, Queens, and Jacks. Each of these cards has 2 faces. Some of these 12 cards have two eyes showing on both faces, and the rest have one eye showing on both faces. How many cards have one eye showing on both faces if the total number of eyes showing on the 12 cards is 42?

Answer 1

[AI-generated answer — Bot]

6 cards have one eye showing on both faces.

Answer 2

hey

Answer 3

anyone on rn?

Answer 4

[AI-generated answer — Explain Bot]

To find the answer, we can use a system of equations.

Let's denote:
x = the number of cards with two eyes showing on both faces
y = the number of cards with one eye showing on both faces

We know that there are 12 cards in total. So we can write the equation:

x + y = 12 (Equation 1)

We also know that the total number of eyes showing on the 12 cards is 42. Each card with two eyes showing contributes 4 eyes (since each card has 2 faces with 2 eyes each), while each card with one eye showing contributes 2 eyes (since each card has 2 faces with 1 eye each). So we can write a second equation:

4x + 2y = 42 (Equation 2)

Now we have a system of linear equations with two variables (x and y). We can solve this system using any method like substitution, elimination, or graphing.

Let's solve it by elimination method:
Multiply Equation 1 by 2:
2x + 2y = 24 (Equation 3)

Now subtract Equation 3 from Equation 2:
4x + 2y - (2x + 2y) = 42 - 24
2x = 18
x = 9

Substitute the value of x back into Equation 1:
9 + y = 12
y = 12 - 9
y = 3

So, there are 3 cards with one eye showing on both faces.