A store clerk sold 25 maths books and 10 english books for $855.00 .if she sold 10 maths books and 40 English books, she would have got $135 more. calculate the cost of each book.
Let m be the math book cost (in dollars) and e be the english book cost (also in dollars). Solve these two equations simultaneously:
25m + 10e = 855
10m + 40e = 855 + 135 = 990
100m + 40e = 3420
90m = 2430
m = 27
Let's assume the cost of a math book as "m" and the cost of an English book as "e".
According to the given information:
25m + 10e = $855 --- Equation 1
10m + 40e = $855 + $135 --- Equation 2
Simplifying Equation 2:
10m + 40e = $990 --- Equation 3
To solve the equations, we can use the method of substitution or elimination. Let's use the elimination method.
Multiply Equation 1 by 4 to make the coefficients of 'e' in both equations match:
(4 * (25m + 10e)) = (4 * $855)
100m + 40e = $3,420 --- Equation 4
Now, subtract Equation 3 from Equation 4:
100m + 40e - (10m + 40e) = $3,420 - $990
90m = $2,430
Divide both sides of the equation by 90:
m = $2,430 / 90
m ≈ $27
Now substitute the value of 'm' into Equation 1 to find the value of 'e':
25m + 10e = $855
25($27) + 10e = $855
675 + 10e = $855
Subtract 675 from both sides of the equation:
10e = $855 - $675
10e = $180
Divide both sides of the equation by 10:
e = $180 / 10
e = $18
Therefore, the cost of each math book is approximately $27, and the cost of each English book is approximately $18.
To solve this problem, let's assign variables to represent the cost of a math book and the cost of an English book.
Let's say the cost of a math book is M and the cost of an English book is E.
According to the information given, the store clerk sold 25 math books and 10 English books for a total of $855. We can write an equation for this scenario:
25M + 10E = 855 ----(Equation 1)
The problem also informs us that if the clerk sold 10 math books and 40 English books, she would have received $135 more. We can write an equation for this scenario as well:
10M + 40E = 855 + 135 ----(Equation 2)
Now, we have a system of two equations with two variables (M and E). We can solve this system using any method such as substitution or elimination.
Let's use the elimination method:
Multiply Equation 1 by 4:
100M + 40E = 3420 ----(Equation 3)
Subtract Equation 2 from Equation 3:
100M + 40E - (10M + 40E) = 3420 - 990
90M = 2430
Divide both sides of the equation by 90:
M = 2430 / 90
M = $27
Now substitute the value of M back into Equation 1:
25 * 27 + 10E = 855
675 + 10E = 855
Subtract 675 from both sides of the equation:
10E = 855 - 675
10E = 180
Divide both sides of the equation by 10:
E = 180 / 10
E = $18
So, the cost of each math book is $27, and the cost of each English book is $18.