At a book fair; three books and two magazines cost $7. Two books and five magazines cost $6.50. Find the cost of a book and the cost of a magazine.
3b + 2m = 7 ---times 2 ---> 6b + 4m = 14
2b + 5m = 6.5 --times 3--> 6b + 15m = 19.5
subtract them:
11m = 5.5
m = .50
sub into first:
3b + 2(.50) = 7
3b = 6
b = 2
Books cost $2 each and magazines cost 50 cents each
(wow, good prices, old textbook ??)
3b + 2m = 7
2b + 5m = 6.50
solve the system by substitution or elimination
2nd eqn times 3/2...3b + 15/2 m = 9.75
subtracting (to eliminate b)
... 5/2 m = 3.25
correction ... 5/2 m = 2.25
To find the cost of a book and the cost of a magazine, we can set up a system of equations based on the given information.
Let's assume that the cost of a book is represented by 'b' and the cost of a magazine is represented by 'm'.
From the first statement, we know that three books and two magazines cost $7. This can be represented by the equation:
3b + 2m = 7 ... (Equation 1)
From the second statement, we know that two books and five magazines cost $6.50. This can be represented by the equation:
2b + 5m = 6.50 ... (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of 'b' and 'm'.
To solve this system, we can use the method of substitution or elimination. Let's solve it using the elimination method:
Multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of 'b' in both equations cancel each other out when added.
2 * (3b + 2m) = 2 * 7
3 * (2b + 5m) = 3 * 6.50
This gives us:
6b + 4m = 14 ... (Equation 3)
6b + 15m = 19.50 ... (Equation 4)
Now, subtract Equation 3 from Equation 4 to eliminate 'b':
(6b + 15m) - (6b + 4m) = 19.50 - 14
11m = 5.50
Divide both sides of the equation by 11:
m = 5.50 / 11
m = 0.50
We have found that the cost of a magazine is $0.50.
Now, substitute the value of 'm' back into Equation 1 or Equation 2 to find the value of 'b'.
Let's use Equation 1:
3b + 2(0.50) = 7
3b + 1 = 7
3b = 7 - 1
3b = 6
b = 6 / 3
b = 2
We have found that the cost of a book is $2.
Therefore, the cost of a book is $2 and the cost of a magazine is $0.50.