a bank loaned out $2,500, part of it at the rate of 7% annual interest, and the rest at 5% annual interest…

a bank loaned out $2,500, part of it at the rate of 7% annual interest, and the rest at 5% annual interest. the total interest earned for both loans was $145.00. how much was loaned at each rate? $ was loaned at 7% and $ was loaned at 5%. question help: video written example message instructor submit question question 20 a candy distributor needs to mix a 30% fat - content chocolate with a 40% fat - content chocolate to create 100 kilograms of a 38% fat - content chocolate. how many kilograms of each kind of chocolate must they use? a) write an equation that uses the information as it is given above that can be used to solve this problem. use x as your variable to represent the quantity of 30% fat - content chocolate. equation: b) answer: they must mix kilograms of the 30% chocolate and kilograms of the 40% chocolate. question help: message instructor

a bank loaned out $2,500, part of it at the rate of 7% annual interest, and the rest at 5% annual interest. the total interest earned for both loans was $145.00. how much was loaned at each rate? $ was loaned at 7% and $ was loaned at 5%. question help: video written example message instructor submit question question 20 a candy distributor needs to mix a 30% fat - content chocolate with a 40% fat - content chocolate to create 100 kilograms of a 38% fat - content chocolate. how many kilograms of each kind of chocolate must they use? a) write an equation that uses the information as it is given above that can be used to solve this problem. use x as your variable to represent the quantity of 30% fat - content chocolate. equation: b) answer: they must mix kilograms of the 30% chocolate and kilograms of the 40% chocolate. question help: message instructor

Answer

Question 19

Explanation:

Step1: Let the amount loaned at 7% be $x$.

Then the amount loaned at 5% is $2500 - x$.

Step2: Calculate the interest from each loan.

The interest from the 7% - loan is $0.07x$, and the interest from the 5% - loan is $0.05(2500 - x)$.

Step3: Set up the interest - total equation.

$0.07x+0.05(2500 - x)=145$.

Step4: Expand and simplify the equation.

$0.07x + 125-0.05x=145$. Combining like terms: $(0.07x - 0.05x)+125 = 145$, so $0.02x+125 = 145$.

Step5: Solve for $x$.

Subtract 125 from both sides: $0.02x=145 - 125=20$. Divide both sides by 0.02: $x=\frac{20}{0.02}=1000$.

Step6: Find the amount loaned at 5%.

The amount loaned at 5% is $2500 - x=2500 - 1000 = 1500$.

Answer:

$1000$ was loaned at 7% and $1500$ was loaned at 5%.

Question 20

Explanation:

Step1: Set up the equation based on fat - content.

Let $x$ be the quantity of 30% fat - content chocolate. Then the quantity of 40% fat - content chocolate is $100 - x$. The fat - content equation is $0.3x+0.4(100 - x)=0.38\times100$.

Step2: Expand and simplify the equation.

$0.3x + 40-0.4x=38$. Combining like terms: $(0.3x - 0.4x)+40 = 38$, so $-0.1x+40 = 38$.

Step3: Solve for $x$.

Subtract 40 from both sides: $-0.1x=38 - 40=-2$. Divide both sides by $-0.1$: $x=\frac{-2}{-0.1}=20$.

Step4: Find the quantity of 40% fat - content chocolate.

The quantity of 40% fat - content chocolate is $100 - x=100 - 20 = 80$.

Answer:

A) Equation: $0.3x+0.4(100 - x)=0.38\times100$ B) They must mix 20 kilograms of the 30% chocolate and 80 kilograms of the 40% chocolate.