Mrs. Crawford has invested $ 6,000 at 3% interest. How much additional money should she invest at 8% interest so that the total income will be 4% of her total investment?
Scott asked you to make 10 gal. of fruit punch that contains 85% fruit juice by mixing together some Sweet Tropical Fruit Punch and some apple juice. How much of each ingredient do you need if the Sweet Tropical Fruit Punch contain 25% juice?
Thank you so much for your help
additional amount --- x
total amount invested = 6000+x
interest from that total at 4% = .04(6000+x)
.03(6000) + .08x = .04(6000+x)
multiply by 100
3(6000+x) + 8x = 4(6000+x)
carry on ...
2nd:
amount of apple juice --- x gal
amount of STFP --- 10-x
x + .25(10-x) = .85(10)
solve for x, etc
Thank you Reiny for your help
You're welcome! I'd be happy to help with your questions.
1. Let's solve the first problem step by step:
To find the additional amount of money Mrs. Crawford should invest, we need to calculate how much total investment is needed at 4% interest.
Step 1: Calculate the income earned from the $6,000 investment at 3% interest:
Income = Principal x Rate
Income = $6,000 x 0.03 = $180
Step 2: Calculate the total investment needed at 4% interest:
Total Investment = Income / Rate
Total Investment = $180 / 0.04 = $4,500
Step 3: Calculate the additional amount Mrs. Crawford should invest at 8% interest:
Additional Investment = Total Investment - Current Investment
Additional Investment = $4,500 - $6,000 = -$1,500
Based on the calculations, Mrs. Crawford would need to invest an additional -$1,500 at 8% interest to achieve a total income of 4% of her total investment. This means she should either reduce her current investment or reassess her investment strategy.
2. Now let's move on to the second problem:
Step 1: Determine the desired quantity of fruit juice in the punch:
10 gal. x 85% = 8.5 gal. of fruit juice
Step 2: Determine the quantity of juice in Sweet Tropical Fruit Punch:
Let's assume we need x gallons of Sweet Tropical Fruit Punch.
The juice content in Sweet Tropical Fruit Punch is 25%, so the quantity of juice from this ingredient is x gallons x 25% = 0.25x gallons.
Step 3: Determine the quantity of apple juice:
The total quantity of juice in the punch is the sum of the juice from both ingredients:
0.25x gallons + (10 - x) gallons = 8.5 gallons
Simplifying the equation:
0.25x + 10 - x = 8.5
Combine like terms:
0.25x - x = 8.5 - 10
-0.75x = -1.5
Divide both sides by -0.75 to isolate x:
x = (-1.5) / (-0.75) = 2
Therefore, you would need 2 gallons of Sweet Tropical Fruit Punch and (10 - 2) = 8 gallons of apple juice to make 10 gallons of fruit punch containing 85% fruit juice.
I hope that helps! Let me know if you have any further questions.