Algebra, word problem

Question

Maroon 5's pet sitting company charges a base fee of $5 and $5 per day. One Direction's pet sitting company charges a base fee of $9 and $3 per day. How long will it be until both companies charge the same price.

Answer 1

Simply write an equation representing the cost for each pet sitting company, set them equal to each other, and solve for the number of days it will take in order for both companies to cost the same amount. I demonstrated these steps below; take a look!

Maroon 5's pet sitting company cost in dollars = 5 + 5d, where d represents the number of days.

One Direction's pet sitting company cost in dollars = 9 + 3d, where d represents the number of days.

Maroon 5's pet sitting company cost in dollars = One Direction's pet sitting company cost in dollars

when 5 + 5d = 9 + 3d

–3d –3d

5 + 2d = 9

–5 –5

2d = 4

d = 2

Therefore, it will take two days for the companies to charge the same price. Done!

Answer 2

p1 = 5t +5, p2 = 3t +9, p1 = p2, 5t+5 = 3t +9; 5t -3t = 9 - 5, 2t = 4, t = 2.

In 2 days these componies charge equel prise.

Answer 3

d = number of days

5 + 5d = 9 + 3d

-3d. -3d

5 + 2d = 9

-5 -5

2d = 4

÷2 ÷2

d = 2

The company prices will be equal in TWO days.

Answer 4

The fee schedule for each pet sitting company can be modelled by the linear equation of cost = (cost per day) days + starting fee. They will charge the same price on day d; which can be solved for by setting expressions for each service equal. The equation for Maroon 5's service is cost = 5d+5. The equation for One Direction's service is cost = 9d + 3. Set these equal: 5d+5 = 9d + 3

Subtract 3 from both sides: 5d + 2 =9d

Subtract 5d from both sides: 2 = 4d

divide by 4 and d = 1/2.

Since the value for d is not a whole number they will never charge the same price. Since one must use the service for at least one day the price for One Direction will always be larger since 1 > 1/2; and 1/2 is the point of equality between where One Direction is less than Maroon5's and greater than Maroon5's. One Direction < Macroon5's at less than 1/2 days and One Direction > Macroon5's at greater than 1/2 days.

This can easily be seen in a chart:

Day number Maroon5's One Direction

1 $10 $12

2 $15 $21

3 $20 $30

4 $25 $39