You have an allowance to spend on lunch this week. You will spend the same amount each day, and you get to keep whatever is left at the end of the week. After two days, you have $12.10 left. After five days, you have $2.50 remaining

Step-by-step explanation:

Each day, the same amount is spent.

Let X be the initial amount at the beginning of the week, T be the amount spent per day.

i. X - 2T = $12.1

ii. $12.1 - 3T = $2.5

Solving ii,

3T = 12.1 - 2.5

T = 9.6/3

= 3.2

Inputting this value in i,

X = 12.1 + (3.2 * 2)

= $18.5

In slope - intercept form, y = mx + c

Slope, m = y2 - y1/x2 - x1

= 2.5 - 12.1/5 - 2

= $-3.2 / day

y = - 3.2x + 18.5.

The total allowance is $18.5, and the amount spent daily is $3.2

Step-by-step explanation:

let T and x represent the total allowance and the amount spent daily respectively.

It was started that the amount remaining after 2 days is $12.10, which implies the person has spend an equal amount for 2 days

T - 2x = 12.10 (equation 1)

It was started that the amount remaining after 5 days is $2.50, which also implies the person has spend an equal amount for 5 days

T - 5x = 2.5 (equation 2)

subtract equation 2 from 1

T - 2x - (T - 5x) = 12.10 - 2.5

T - 2x - T + 5x = 9.6

3x = 9.6

Divide both side by 3

x = 9.6/3 = 3.2

from equation 1

T - 2x = 12.10

T = 12.10 + 2x = 12.10 + 2*3.2

= 12.10 + 6.4 = 18.5