Question

Question 4

4 pts
Tom and Larry put money into their bank account each week. The table below shows Tom's
saving habits.
Weeks
1
2.
3
4
5
Account Balance ($)
18 30 42 54 66
Larry's saving habits can be represented by the equation y = 15x + 5, where y is money in
his account and x is the number of weeks that he has been saving.
a. How much money was initially in Tom's account? [Select]
b. How much money was initially in Larry's account (Select]
c. Who is saving money at a faster rate? (Select ]
d. When will Tom have more money in his account than Larry?
[ Select ]

Answer 1

a) The initial amount of money in Tom's account is $18. b) The initial amount of money in Larry's account is $5. c) Larry is saving money at a faster rate. d) Tom will have more money than Larry after approximately 4.33 weeks.

Step-by-step explanation:

a) To find the initial amount of money in Tom's account, we can look at the account balance at week 1, which is $18.

b) To find the initial amount of money in Larry's account, we can substitute x=0 into the equation y = 15x + 5. This gives us y = 15(0) + 5 = 5.

c) To compare their saving rates, we can compare the coefficients of x in their equations. Tom's saving rate is $12 per week (the difference between each balance), while Larry's saving rate is $15 per week. Thus, Larry is saving money at a faster rate.

d) To find when Tom will have more money than Larry, we can set their account balances equal to each other: 12x + 18 = 15x + 5. By rearranging the equation, we get 18 - 5 = 15x - 12x. Simplifying further, we have 13 = 3x, and dividing both sides by 3 gives x = 13/3. Therefore, Tom will have more money than Larry after approximately 4.33 weeks.

Answer 2

(a). 6 ; (b). $5 ; (c). Larry'c ; (d) at time they open their accounts.

Step-by-step explanation:

Larry's saving habits is
`y_(L)` = 15x + 5

Tom's saving habits:

m = (30 - 18) / (2 - 1) = 12 and b = 18 - 12 = 6

`y_(T)` = 12x + 6

(a). $6

(b). $5

(c). Larry'c (
`m_(L)` = $15 ,
`m_(T)` = $12 )

(d). When
`y_(T)` >
`y_(L)` ?

15x + 5 < 12x + 6

3x < 1

x <
`(1)/(3)` of
`1^(st)` week ( x ∈ [0, 1) )⇒ Tom will have more money in his account than Larry at time they open their accounts.