Question

Write an equation for each context. Draw a model first if necessary, and make sure you define your variable and what it represents.a. Tom has $12,484 in his bank account. Six months ago, he had $1,240. How much does Tom get paid each month if he has only deposited his monthly paycheck into his account?b. Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box. The third box contained two more pounds than the first box. The last box contained one-fourth the amount in the second box. How much candy was in each box?c. Simon is ordering equipment for his tennis team. He orders a racquet and can of three tennis balls for each player. Each can of balls costs $4. For a team of 5 players, his bill total is $415. How much does each racquet cost?

Answer 1

Answer:

(a)$2248.8

(b) 14, 28, 16 and 7 candies

(c) $79

Step-by-step explanation:

(a) the model can be represented by the nth term of an arithmetic progression

L = a + (n-1)d

L= the amount in his account after 6 month; $12484

a= the amount in his account six month before; $1240

n = 6, being the sixth month of his deposit

d = the amount deposited monthly

12484 = 1240 + 5d:

12484-1240 = 5d

5d= 11244

d = 2248.8

(b) let the 1st box contain = x

2nd = 2x; 3rd = x + 2, 4th = 1/4(2x)

Hence; x + 2x + x +2 + 1/4(2x) = 65

4x + x/2 = 65-2

9x/2 = 63 ; 9x = 126. ; x = 14

(c) Each player gets a racket (r) and a can (c) of balls

The 5 players get in all 5 racket + 5 cans since Simon is a member

Therefore, 5r + 5c = 415

But each can cost $4,

5r + 5* 4 = 415; 6r = 415-20

5r = 395 ; r = 395/5

r = $ 79

The racket cost $79 each.