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

a.
`6x+1240=12484`

b.

`x_1+x_2+x_3+x_4=65\\x_2=2x_1\\x_3=x_1+2\\x_4=0.25x_2`

c.
`5x+20=415`

Explanation:

a. In the account are 6 deposits of the paid that Tom gets each month and the initial $1240. Let
`x` be the paid Tom gets each month, then:

`6x+1240=12484`

Solving for
`x`:

`6x=12484-1240\\6x=11244\\x=(11244)/(6) \\x=1874\\`

b)Let
`x_1` be pounds contained in the first box,
`x_2` the pound in the second box,
`x_3` the pounds in the third box and
`x_4` the pound in the fourth box, then:

`x_1+x_2+x_3+x_4=65\\x_2=2x_1\\x_3=x_1+2\\x_4=0.25x_2`

Substitute the value of
`x_2` in the last equation:

`x_4=0.25(2x_1)\\x_4=0.5x_1`

Substitute all the equation in the first and solve for
`x_1`:

`x_1+(2x_1)+(x_1+2)+(0.5x_1)=65\\4.5x_1=65-2\\x_1=63/4.5=14`

Solving for x2,x3, and x4:

`x_2=2x_1=2*14=28\\x_3=x_1+2=14+2=16\\x_4=0.25x_2=0.25*28=7`

c) Simon is ordering 5 cans and 5 racquets, the total from the cans is 5(4)=$20. Let x be the cost of each racquet,

`5x+20=415`

Solving for x:

`5x=415-20\\x=395/5=79`