Angela uses 2/3 cups of strawberries to make 5/6 of a liter of smoothie. What is the unit rate in cups of strawberries per liter

To calculate this, a specific formula will be necessary. Years = log (total/principal) / [n * log (1 + rate / n)]. Part A) For Calvin: $400 at 5% monthly results in $658.80; Time =? Monthly compounding, n = 12. Thus, Years = log(658.80/400) / [12 * log(1+ (.05/12))]. Subsequently, Years = log( 1.647) / (12 * log(1.0041666667)). Then, Years = 0.21669359917 / 12 * 0.0018058008777. Thus resulting in Years = 0.21669359917 / 0.0216696105. Ultimately, Years ≈ 9.999884362. Part B) For Makayla: $300 at 6% quarterly yields $613.04; Time=? Quarterly compounding, n = 4. Therefore, Years = log(613.04/300) / [4 * log (1 +.06/4)]. This results in Years = log(2.0434666667) / (4 * log(1.015)). Years thus equals 0.31036755784 / (4 * 0.0064660422492), resulting in Years ≈ 11.9999044949. The approximate difference is about 3 years.

Jane must lower the price by 20%

Let C denote the quantity of compost

T represent the quantity of topsoil

Each cubic yard of compost is priced at $25

Thus, the cost of C cubic yards of compost is 25C

Each cubic yard of topsoil costs $15

Therefore, the cost for T cubic yards of topsoil is 15T

Together, the amount of compost plus topsoil equals 10

C + T = 10 -------> Equation 1

The total cost for compost and topsoil is $180

25C + 15T = 180 --------> Equation 2

Rearranging the first equation to find C

C + T = 10

results in

C = 10 - T

Now substitute into the second equation

25C + 15T = 180

25 ( 10 - T) +15T = 180

Using like terms: 250 - 25T + 15T = 180

From which we can simplify to 250 - 10T = 180 by removing 250 from both sides

-10T = 180 - 250

yielding -10T = -70 (dividing both sides by -10)

results in T = 7