Please help with the following questions ab Thanks in advanc

Please help with the following questions a&b. Thanks in advance.

Twenty students participated in a math competition. Each student finished in the top three of their respective event. The students scored total of 105 points. A first-place finish scores 10 points, a second-place finish scores 5 points, and a third-place finish scores 1 point. The number of third-place finishes is equal to the sum of the number of first- and second-place finishes. Which system of equation can be used to find x, the number of first-place finishes, y, the number of second-place finishes, and z the number of third-place finishes? A. {x + y + z = 20 x + y + = 105 x + z = y B. {x + y + z = 20 10x + 5y + z = 105 x + z = y C. {x + y + z = 105 10x + 5y + z = 105 x + z = y D. {x + y + z = 20 10x + 5y + z = 105 x + z = y b. The deer population in an area is increasing by about 2.5%each year, The initial population was 2537. Assuming that the population increases at the same rate for the next few years, which formula expresses the number of years from last year, t, in terms of the deer population, p? A. t = log 2537 - log p/log 1.025 B. t = log p - log 1.025/log 2537 C. log p - log 2537/log 1.025

Solution

a) twenty students participate : x +y +z = 20 ---(1)

a first place scores 10 points: 10 x

second place scores 5 points 5y

third place scores 1 point z

So, 10x + 5y +z = 105 ---(2)

No. 3rd place = um of 1st place and second place

z = x+y

z - x = y ---(3)

b) Intuial popoualtion = 2537

rate of increase = 2.5%

Pupulation after t years can be give as:

p = 2537(1.025)^t

(p/2537) = 1.025^t

take natural log on bith sides:

ln(p/2537) = t*ln(1.025)

t = (lnp - ln2537)/ln1.025