A coffee mixture has beans that sell for $0.72 a pound and beans that sell for $0.52. If 110 pounds of beans create a mixture worth $0.74 a pound, how much of each bean is used? Model the scenario then solve it. Then, in two or more sentences explain whether your solution is or is not reasonable.
Suppose Johnny invests $41,745 into an account, which has been earning interest for many years and he now has a total of $39,974. In two or more sentences explain why a negative number would/wouldn’t be reasonable in the solution of the rate of the investment.
I got question ones to answer
The price of each type of beans is such that it is impossible to create a mixture of which price is higher than the highest ingredient price. In this case, we have one type of bean that costs $0.72 and one that costs $0.52 per pound. Even if the mixture is made purely out of the first type of beans it wouldn't cost $0.74 per pound. In general, you solve this problem using this system of equations: x + y = 110 x*0.72 + y*0.52 = 0.74 * 100
thanks
yes
To solve the coffee mixture problem, let's assume that x pounds of the $0.72 beans and (110 - x) pounds of the $0.52 beans are used. The total cost of the mixture can be calculated by multiplying the weight of each bean by its respective price and then adding the two values together. So we have the equation:
0.72x + 0.52(110 - x) = 0.74 * 110
Solving this equation will give us the value of x, which represents the pounds of $0.72 beans used.
To solve the investment problem, we can use the formula for calculating compound interest:
Amount = Principal * (1 + Rate)^Time
In this case, the principal is $41,745 and the final amount is $39,974. We need to solve for the rate. We can rearrange the formula to solve for the rate:
Rate = (Amount / Principal)^(1/Time) - 1
Plugging in the given values will give us the rate of the investment.
For the coffee mixture problem, we can evaluate the reasonability of our solution by checking if the pounds of each bean are within the reasonable range. It is unlikely that we would use negative pounds of beans, so our solution should yield positive values within the given weight limit of 110 pounds.
For the investment problem, a negative number would not be reasonable in the solution of the rate of the investment. The rate represents the percentage of interest gained over time, and it cannot be negative as it implies a loss rather than a gain.