If 7 cartons of apple juice and 2 cartons of grapefruit juice cost £6.15 and 5 cartons of apple juice and 8 cartons of gratefruit juice cost £9.19
calculate the cost of 2 cartons of apple juice and 5 grapefruit juice
Using Algebraic calculation
the cost of 2 cartons of apple juice and 5 grapefruit juice is £4.99
Well, solving this math problem won't be a "fruitful" endeavor without some algebraic calculations!
Let's assign variables to the unknowns:
Let's say the cost of each carton of apple juice is A, and the cost of each carton of grapefruit juice is G.
From the given information, we can set up two equations:
Equation 1: 7A + 2G = 6.15 (because 7 cartons of apple juice and 2 cartons of grapefruit juice cost £6.15)
Equation 2: 5A + 8G = 9.19 (because 5 cartons of apple juice and 8 cartons of grapefruit juice cost £9.19)
Now, let's solve this "juicy" problem using a method called substitution.
From Equation 1, let's solve for A by isolating it:
7A + 2G = 6.15
7A = 6.15 - 2G
A = (6.15 - 2G)/7
Now, let's substitute this value of A into Equation 2:
5(6.15 - 2G)/7 + 8G = 9.19
Now, let's simplify this equation a bit:
30.75 - 10G/7 + 8G = 9.19
Let's multiply both sides of the equation by 7 to get rid of the fractions:
30.75 - 10G + 56G = 64.33
Now, let's combine like terms:
46G = 33.58
Finally, divide both sides by 46 to solve for G:
G = 33.58/46
G ≈ 0.73
Now that we know the cost of each carton of grapefruit juice, we can substitute this value back into Equation 1 to find the cost of each carton of apple juice:
7A + 2(0.73) = 6.15
Simplifying this equation gives us:
7A + 1.46 = 6.15
Subtracting 1.46 from both sides:
7A ≈ 4.69
Finally, divide both sides by 7 to solve for A:
A ≈ 0.67
So, the cost of 2 cartons of apple juice and 5 cartons of grapefruit juice is approximately £0.67 x 2 + £0.73 x 5 = £1.34 + £3.65 = £5.99.
Voila! The grand "total juice" cost is £5.99.
To solve this problem using algebraic calculation, we can assign variables to the unknown quantities. Let's assume x represents the cost of one carton of apple juice, and y represents the cost of one carton of grapefruit juice.
From the given information, we know that:
7x + 2y = £6.15 (1)
5x + 8y = £9.19 (2)
To find the cost of 2 cartons of apple juice and 5 cartons of grapefruit juice, we need to find the value of 2x + 5y.
To eliminate one of the variables, let's multiply equation (1) by 4 and equation (2) by 1:
28x + 8y = £24.60 (3)
5x + 8y = £9.19 (2)
Now, we can subtract equation (2) from equation (3) to eliminate the y variable:
(28x + 8y) - (5x + 8y) = £24.60 - £9.19
23x = £15.41
Divide both sides of the equation by 23 to solve for x:
x = £15.41 / 23
x ≈ £0.67
Now that we have the value of x, we can substitute it back into equation (1) to solve for y:
7x + 2y = £6.15
7(0.67) + 2y = £6.15
4.69 + 2y = £6.15
2y = £6.15 - £4.69
2y ≈ £1.46
y ≈ £0.73
Therefore, the cost of 2 cartons of apple juice and 5 cartons of grapefruit juice would be:
2x + 5y = 2(£0.67) + 5(£0.73) ≈ £1.34 + £3.65 ≈ £4.99.
x = 0.67
X = 0.64
7 a + 2 g = 6.15 ... multiplying by 4 ... 28 a + 8 g = 24.60
5 a + 8 g = 9.19
solve the system for a and g
subtract equations to eliminate g
... solve for a
substitute back to find g