how many quetions are needed to get a coloring book.
s+b+2c=26
4s=8
3b+c=22
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.
To determine the number of questions needed to get a coloring book, let's solve the system of equations you provided:
1) s + b + 2c = 26
2) 4s = 8
3) 3b + c = 22
Let's start solving the equations one by one:
Equation 2) 4s = 8
Divide both sides of the equation by 4 to isolate s:
s = 8/4
s = 2
Now we can substitute this value of s into equation 1) to simplify it further:
1) 2 + b + 2c = 26
Rearrange the equation:
b + 2c = 26 - 2
b + 2c = 24
Now we have a simplified form of equation 1).
Moving on to equation 3), we will substitute the value of s we found earlier:
3) 3b + c = 22
Replace s with 2:
3b + c = 22
We now have two equations with two variables: b and c. Let's solve them simultaneously using the elimination or substitution method:
To eliminate the variable c, we'll multiply equation 1) by 3 and equation 2) by 2:
(3) b + 2c = 24 (multiply by 2)
(2) 6b + 2c = 44 (multiply by 3)
Now subtract equation 1) from equation 2) to eliminate the variable c:
(2) 6b + 2c - (3) b + 2c = 44 - 24
6b + 2c - 3b - 2c = 20
3b = 20
b = 20/3
Now substitute the value of b we found back into equation 1) to find c:
(1) 2 + b + 2c = 26
2 + 20/3 + 2c = 26
6 + 20 + 6c = 78
26 + 6c = 78
6c = 78 - 26
6c = 52
c = 52/6
c = 8 2/3
Now we have found the values of b and c. The number of questions needed to get a coloring book can be calculated by using the equation:
s + b + 2c = 26
2 + 20/3 + 2(8 2/3) = 26
To calculate this expression, we need to convert the mixed fraction 8 2/3 into improper fraction form:
b + 2c = 26
2 + 20/3 + 2(26/3)
2 + 20/3 + 52/3
(2*3 + 20 + 52)/3
(6 + 20 + 52)/3
(78)/3
26
Therefore, the number of questions needed to get a coloring book is 26.
To find the number of questions needed to get a coloring book, we need to solve the given system of equations:
Equation 1: s + b + 2c = 26
Equation 2: 4s = 8
Equation 3: 3b + c = 22
Let's solve the equations step-by-step:
Step 1: Simplify Equation 2
Divide both sides of Equation 2 by 4
4s/4 = 8/4
s = 2
Step 2: Substitute s = 2 into Equation 1
2 + b + 2c = 26
b + 2c = 26 - 2
b + 2c = 24
Step 3: Substitute s = 2 into Equation 3
3b + c = 22
3b + c = 22
Step 4: Multiply Equation 2 by 3
3(3b + c) = 3 * 22
9b + 3c = 66
Step 5: Multiply Equation 1 by 9
9(b + 2c) = 9 * 24
9b + 18c = 216
Step 6: Subtract Equation 4 from Equation 5
(9b + 18c) - (9b + 3c) = 216 - 66
9b - 9b + 18c - 3c = 150
15c = 150
Step 7: Divide both sides by 15
15c/15 = 150/15
c = 10
Step 8: Substitute c = 10 into Equation 3
3b + 10 = 22
3b = 22 - 10
3b = 12
Step 9: Divide both sides by 3
3b/3 = 12/3
b = 4
Therefore, to get a coloring book, you would need to answer 2 questions (s = 2), buy 4 books (b = 4), and collect 10 coins (c = 10).