5kg of flour and 4kg of sugar cost $14.80. If 3/4kg of flour cost as much as 3/5kg of sugar, what is the cost of 1kg of sugar?
x = cost of 1kg flour
y = cost of 1kg sugar
5x + 4y = $ 14.80
x = (14.80 - 4y)/5
3x/4 = 3y/5
(3/4)*[(14.80 - 4y)/5] = 3y/5
2.22 - 0.6y = 0.6y
1.2y = 2.22
y = $1.85
x = $1.48
To solve this problem, we can set up a system of equations.
Let's assume the cost of 1kg of flour is 'x' and the cost of 1kg of sugar is 'y'.
From the given information, we know that:
5kg of flour + 4kg of sugar = $14.80
This can be expressed as:
5x + 4y = 14.80 ----- Equation (1)
We also know that:
3/4kg of flour = 3/5kg of sugar
We can express this as an equation:
(3/4)x = (3/5)y
To eliminate the fractions, we can multiply both sides of the equation by 20:
20 * (3/4)x = 20 * (3/5)y
This simplifies to:
15x = 12y ----- Equation (2)
Now we have a system of two equations (Equations 1 and 2). We can solve this system to find the values of x and y.
Let's multiply Equation (2) by 4 so that the coefficients of 'y' in both equations are the same:
4 * 15x = 4 * 12y
60x = 48y
Now we can substitute this value of 'y' into Equation (1):
5x + 4(60x/48) = 14.80
Simplifying further:
5x + 5x = 14.80
10x = 14.80
x = 14.80/10
x = $1.48
So, the cost of 1kg of flour is $1.48.
Now we can substitute the value of 'x' into Equation (2) to find the value of 'y':
15(1.48) = 12y
22.2 = 12y
y = 22.2/12
y ≈ $1.85 (rounded to the nearest cent)
Therefore, the cost of 1kg of sugar is approximately $1.85.