5 pens and 3 rulers cost a total of £1.22
3 pens and 6 rulers cost a total of £1.53
How much does each pen and each ruler cost?
A) 5 p + 3 r = 1.22
B) 3 p + 6 r = 1.53
solve the system
... multiplying A) by 2 ... 10 p + 6 r = 2.44
... subtracting B) ... 7 p = 2.44 - 1.53
solve for p , then substitute back to find r
Let's assume the cost of each pen is P and the cost of each ruler is R.
From the first statement, we know that 5P + 3R = £1.22.
From the second statement, we know that 3P + 6R = £1.53.
To solve this system of equations, we can use the method of substitution.
Let's solve equation 1 for P:
5P + 3R = £1.22
5P = £1.22 - 3R
P = (£1.22 - 3R)/5
Now, we can substitute this expression for P into equation 2:
3(£1.22 - 3R)/5 + 6R = £1.53
Let's simplify this equation step-by-step:
Multiply both sides by 5 to get rid of the denominators:
3(£1.22 - 3R) + 30R = 5(£1.53)
3£1.22 - 9R + 30R = 5£1.53
3£1.22 + 21R = 5£1.53
£3.66 + 21R = £7.65
Subtract £3.66 from both sides:
21R = £7.65 - £3.66
21R = £3.99
Divide both sides by 21:
R = £3.99/21
R ≈ £0.19
Now that we have the value of R, we can substitute it back into equation 1 to find P:
5P + 3(£0.19) = £1.22
5P + £0.57 = £1.22
5P = £1.22 - £0.57
5P = £0.65
P = £0.65/5
P ≈ £0.13
So, each pen costs approximately £0.13 and each ruler costs approximately £0.19.
To find out how much each pen and each ruler costs, we can set up a system of equations based on the given information.
Let's assume the cost of each pen is 'p' and the cost of each ruler is 'r'.
According to the first statement, 5 pens and 3 rulers cost a total of £1.22, so we can write the equation:
5p + 3r = 1.22
According to the second statement, 3 pens and 6 rulers cost a total of £1.53, so we can write another equation:
3p + 6r = 1.53
Now, we have a system of two equations with two unknowns. To solve this system, we can either use substitution or elimination method.
Let's use the elimination method to solve the system:
Multiply the first equation by 2:
10p + 6r = 2.44
Now, subtract the second equation from this modified first equation:
(10p + 6r) - (3p + 6r) = 2.44 - 1.53
This simplifies to:
7p = 0.91
Divide both sides by 7:
p = 0.91 / 7
p ≈ £0.13 (rounded to two decimal places)
Now, substitute the value of p back into one of the original equations to find r.
Using the first equation:
5p + 3r = 1.22
5(0.13) + 3r = 1.22
0.65 + 3r = 1.22
3r = 1.22 - 0.65
3r = 0.57
Divide both sides by 3:
r = 0.57 / 3
r ≈ £0.19 (rounded to two decimal places)
So, each pen costs approximately £0.13 and each ruler costs approximately £0.19.