Mixing two types of candy, the price of which was $2 and $4 per pound, Ella got a 10-lb mix of candy that cost $2.90 per pound. How many pounds of each kind of candy were used for the mix?
Let x be the number of pounds of the $2 candy and y be the number of pounds of the $4 candy. Then we have:
x + y = 10 (the total weight of the mix is 10 pounds)
2x + 4y = 29 (the total cost of the mix is $2.90 per pound)
Solving the first equation for x, we get:
x = 10 - y
Substituting into the second equation, we get:
2(10 - y) + 4y = 29
Expanding and simplifying, we get:
20 - 2y + 4y = 29
2y = 9
y = 4.5
Substituting back into the equation x + y = 10, we get:
x = 10 - y = 5.5
Therefore, Ella used 5.5 pounds of the $2 candy and 4.5 pounds of the $4 candy for the mix.
Nadya bakes 20 cookies every half hour. Vasil sells 38 cookies per hour. How many cookies are left unsold if the work from 6:00am until noon?
There are a total of 6 - 6 = 0 hours from 6:00am until noon.
In one hour, Nadya can bake:
20 cookies/half hour * 2 half hours/hour = 40 cookies/hour
In one hour, Vasil can sell:
38 cookies/hour
Therefore, in one hour, the number of cookies left unsold is:
40 cookies/hour - 38 cookies/hour = 2 cookies/hour
Since there are 0 hours from 6:00am until noon, the total number of cookies left unsold is:
0 hours * 2 cookies/hour = 0 cookies
Therefore, there are no cookies left unsold if Nadya bakes 20 cookies every half hour and Vasil sells 38 cookies per hour from 6:00am until noon.
To solve this problem, we can use a system of equations.
Let's assume that Ella used x pounds of candy that cost $2 per pound, and y pounds of candy that cost $4 per pound.
According to the given information:
- The total weight of the candy mix is 10 pounds.
- The cost per pound of the mix is $2.90.
Based on the total weight, we can set up the following equation:
x + y = 10 (Equation 1)
Since the price of the mix is the average of the two candy prices, we can set up the following equation:
(2x + 4y) / 10 = 2.90 (Equation 2)
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the substitution method in this case.
From Equation 1, we can solve for x:
x = 10 - y
Now, substitute x in Equation 2 with its value:
(2(10 - y) + 4y) / 10 = 2.90
Simplify the equation:
(20 - 2y + 4y) / 10 = 2.90
(20 + 2y) / 10 = 2.90
20 + 2y = 2.90 * 10
20 + 2y = 29
Subtract 20 from both sides:
2y = 29 - 20
2y = 9
Divide both sides by 2:
y = 9 / 2
y = 4.5
Now, we can substitute the value of y back into Equation 1 to find x:
x + 4.5 = 10
x = 10 - 4.5
x = 5.5
Therefore, Ella used 5.5 pounds of candy that cost $2 per pound and 4.5 pounds of candy that cost $4 per pound for the mix.