Question

Sophia and Emily are twin sisters and best friends. They're saving up for concert tickets and agreed to pay for the tickets together when they have enough money. They both created equations to see how fast they were making money and came up with the following expressions:

Sophia: 35w+55-10w

Emily: 28w+75-5w+12

where 'w' is the number of weeks they have been saving

(a) Combine their expressions to see how much they are making together.

(b) Using the expressions, see if they will have above $350 in four weeks. If not, how much will they be short?

(c) If their friend Becky also wants to join and is making money according to the expression: 50w+25, create a new expression for the total and see if they will have above $525 for the three of them after four weeks.

Answer 1

(b) Using the expressions, see if they will have above $350 in four weeks. If not, how much will they be short?

Answer 2

Here, the given expressions that shows the amount after w weeks,

Sophia : 35w+55-10w

Emily : 28w+75-5w+12

(a) So, the total money created by both = Sophia's money + Emily's money

= 35w+55-10w + 28w+75-5w+12

= 48w + 142

(b) For w = 4,

Their total collection for 4 weeks = 48(4) + 142 = 334 < 350

Hence, they will not have above $350 in four weeks.

And, the amount they need to reach $ 350 = 350 - 334 = $ 16,

Therefore, $ 16 will be short.

(c) Becky's expression : 50w+25

Thus, the new total collection = 48w + 142 + 50w + 25

= 98w + 167

If w = 3,

Total collection after 3 weeks = 98(3) + 167 = $ 461 < $ 525

Thus, they will not have above $525 for the three of them after four weeks.