how many quetions are needed to get a coloring book.

Question

s+b+2c=26
4s=8
3b+c=22

Answer 1

To find the number of questions needed to get a coloring book, you need to solve the system of equations:

s + b + 2c = 26 (Equation 1)
4s = 8 (Equation 2)
3b + c = 22 (Equation 3)

First, solve Equation 2 for s:
4s = 8
Divide both sides by 4: s = 8/4
Simplify: s = 2

Substitute the value of s in Equation 1:
2 + b + 2c = 26
Simplify: b + 2c = 26 - 2
b + 2c = 24 (Equation 4)

Substitute the value of s in Equation 3:
3b + c = 22
Substitute s = 2 in Equation 3:
3b + c = 22
3b + c = 22
Divide the whole Equation 3 by 3:
b + (1/3)c = 22/3 (Equation 5)

To simplify further, multiply Equation 5 by 3 to remove fractions:
3b + c = 22
3(b + (1/3)c) = 22 * 3
3b + c = 66 (Equation 6)

Now, we have two equations:
b + 2c = 24 (Equation 4)
3b + c = 66 (Equation 6)

Multiply Equation 4 by -3:
-3(b + 2c) = -3(24)
-3b - 6c = -72 (Equation 7)

Add Equation 6 and Equation 7:
(-3b - 6c) + (3b + c) = -72 + 66
-3b + 3b - 6c + c = -6
-5c = -6
Divide both sides by -5:
c = -6 / -5
c = 6/5
Simplify: c = 1.2

Substitute the value of c in Equation 4:
b + 2(1.2) = 24
b + 2.4 = 24
b = 24 - 2.4
b = 21.6

Since b = 21.6 is not a whole number, there is no valid solution for the given system of equations. Therefore, we cannot determine the number of questions needed to get a coloring book based on these equations.