Breanna works in the mall and her hours increase during busy shopping times of the year. breanna has a plan to save $25 each week for 5 weeks, and then increase that amount by $20 for the next 7 weeks during the busy time, then go back to $25 per week. if breanna’s plan is to save $540, how many weeks total will she need to save?
a.
11 weeks
b.
16 weeks
c.
22 weeks
d.
23 weeks

Number of weeks Breanna saves are 16 weeks .

Option (b) is correct .

Step-by-step explanation:

As given

Breanna works in the mall and her hours increase during busy shopping times of the year.

Breanna has a plan to save $25 each week for 5 weeks.

Thus

Breanna saves in first 5 weeks = Amount saves per weeks in next 5 weeks × Number of weeks .

                                                    = $25 × 5

                                                   = $ 125  

Increase that amount by $20 for the next 7 weeks during the busy time.

Thus

Amount saves per weeks for next 7 weeks = Amount saves per weeks in first 5 weeks + Increase in amount .

                                                     = $25 +$ 20

                                                     = $ 45

Breanna saves in next 7 weeks = Amount saves per week× Number of weeks .

Put all the values in the above

                                                    = $45 × 7

                                                    = $ 315

As given

Breanna saves $25 per week.

If Breanna’s plan is to save $540 .

Let us assume last weeks in which Breanna saves $25 per weeks be x .

Breanna saves in last x weeks = Amount saves for next x weeks × Number of weeks .    

                                                  = 25 × x

                                                  = 25x

Equation becomes

Breanna saves in first 5 weeks +  Breanna saves in next 7 weeks  + Breanna saves in last x weeks = Total saving amount .

125 +  315 + 25x = 540

440 + 25x = 540

25x = 540 - 440

25x = 100

x = 4 weeks

Thus

Total number of weeks Breanna saves = 5 weeks + 7 weeks + 4 weeks

                                                                 = 16 weeks

Therefore the number of weeks Breanna saves are 16 weeks .

Option (b) is correct .

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,