a shop has one pound bags of peanuts for $2.00 and three-pound bags of peanuts for $5.50 if you buy 5 bags and spend $17, how many of each size bad did you buy?
If there are x $2 bags, then the rest (5-x) are $5.50 bags. So,
2.00x + 5.50(5-x) = 17.00
To find out how many of each size bag you bought, you can use algebraic equations. Let's assume you bought x one pound bags and y three-pound bags.
The given information states that one pound bags cost $2.00, three-pound bags cost $5.50, and you bought 5 bags in total, spending $17.
From this information, we can form the following equations:
1. The total number of bags equation: x + y = 5
2. The total cost equation: 2x + 5.50y = 17
Now we have a system of equations to solve simultaneously to find the values of x and y.
There are a few methods to solve these equations, such as substitution, elimination, or graphing. Let's use the substitution method:
From equation 1, we can express x as x = 5 - y. Now substitute this value of x into equation 2:
2(5 - y) + 5.50y = 17
Simplify the equation:
10 - 2y + 5.50y = 17
Combine like terms:
3.50y = 7
Divide both sides of the equation by 3.50:
y = 2
Now substitute the value of y back into equation 1:
x + 2 = 5
Subtract 2 from both sides:
x = 3
Therefore, you bought 3 one pound bags and 2 three-pound bags.