A shop sells candies by weight. Monisha bought 2 full bags of chocolates and 3 full bags of gummy bears for $23.50. If 3/4 of a bag of chocolate cost as much as 5/6 of a bag of gummy bears, find the cost of 1 full bag of chocolates.
3/4C = 5/6G
Multiply by 6/5.
18/20C = 9/10C = .9C = G
2C + 3G = 23.50
Substitute .9C for G in second equation and solve for C. If you want, you can insert that value into the first equation and solve for G. Check by inserting both values into the second equation.
To find the cost of 1 full bag of chocolates, let's first assign variables to represent the unknowns.
Let's say:
- The cost of 1 full bag of chocolates is x dollars.
- The cost of 1 full bag of gummy bears is y dollars.
We are given the following information:
- Monisha bought 2 full bags of chocolates, so the total cost of the chocolate bags is 2x dollars.
- Monisha bought 3 full bags of gummy bears, so the total cost of the gummy bear bags is 3y dollars.
- The total cost of the chocolates and gummy bears is $23.50, so we can write the equation:
2x + 3y = 23.50 -- Equation 1
We are also given the information that 3/4 of a bag of chocolates costs as much as 5/6 of a bag of gummy bears.
Let's convert these fractions into decimals:
- 3/4 = 0.75
- 5/6 = 0.83 recurring (rounded to two decimal places)
We can set up another equation based on this information:
0.75x = 0.83y -- Equation 2
Now we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of x and y.
To solve the system of equations, we can use the method of substitution. Rearrange Equation 2 to solve for x:
x = (0.83y)/0.75
Substitute this expression for x in Equation 1:
2((0.83y)/0.75) + 3y = 23.50
Now we can solve for y:
(1.66y/0.75) + 3y = 23.50
1.66y + 2.25y = 23.50 * 0.75
3.91y = 17.635
y = 17.635 / 3.91
y ≈ 4.50
Now substitute the value of y back into Equation 2 to find x:
0.75x = 0.83(4.50)
0.75x = 3.735
x = 3.735 / 0.75
x ≈ 4.98
Therefore, the cost of 1 full bag of chocolates is approximately $4.98.