Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Samir is thinking of two numbers. Adding 5 times the first number and 4 times the second number gives a total of 21. Also, adding 5 times the first number and 9 times the second number gives 16. What are the two numbers?

the first number is 3.4 and the second number is 1

Step-by-step explanation:

The computation of the two numbers is shown below:

Let us assume the first number be x

And, the second number be y

Now the equations are

5x + 4y = 21

And,

5x + 9y = 16

Now subtract equation 2 from equation 1

-5y = -5

y = 1

And, the x is

5x + 4 = 21

5x = 17

x = 3.4

Hence, the first number is 3.4 and the second number is 1

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.