(2) The equation c = 50 + 35m shows the amount c that Dina paid for
her health club membership after m months. The table shows
the amount Judy paid for her health club membership.
Number of Months
Amount Judy Paid
0
$80
1
$105
2
$130
3
$155
Which statement is true? Select all that apply.
A Dina paid a higher amount to join the health club.
B Judy pays more per month to be a member.
C After 1 month, Judy has paid more than Dina.
(D) After 4 months, Dina has paid more than Judy.

C, D are true

Step-by-step explanation:

Dina's costs:

Dina paid according to the equation c = 50 + 35m.

When shew joined, the number of the month was 0.

Using 0 for m, we get

c = 50 + 35 * 0

c = 50 + 0

c = 50

Dina paid $50 to join. The since m, the number of months, is being multiplied by 35, she pays $35 per month.

Dina: $50 to join + $35 per month.

Judy's costs:

Judy paid $80 for month 0. That means she paid $80 to join.

In month 1, she had paid a total of $105. Subtract the amount paid at joining, $105 - $80 = $25, and you see that Judy paid $25 per month.

Judy: $80 to join + $25 per month

Now we look at the statements.

A Dina paid a higher amount to join the health club. False. Dina paid $50 which is less than the $80 that Judy paid.

B Judy pays more per month to be a member. False. Judy pays $25 per month which is less than the $35 per month that Dina pays.

C After 1 month, Judy has paid more than Dina. After 1 month, Judy paid $105. After 1 month, Dina paid c = 50 + 35m = 50 + 35 * 1 = 50 + 35 = 85. True. After 1 month, Judy paid $105, which is more than the $85 Dina paid for 1 month.

D After 4 months, Dina has paid more than Judy.

After 4 months, Dina paid c = 50 + 35m = 50 + 35 * 4 = 50 + 140 = 190. After 4 months, Judy paid $25 more than she paid after 3 months. $155 + $25 = $180. After 4 months, Dina paid $190 which is more than the $180 Judy paid. True.

Let us say that:

x = cost of shorts

y = cost of slacks

z = cost of sports coat

From the given statements, we can create the following equations:

eqtn 1: 3 x + y = 10.96

eqtn 2:  7 x + 2 y + z = 30.40

eqtn 3:  4 x + z = 14.45

Rewrite eqtn 1 explicit to y:

y = 10.96 – 3 x                    --> eqtn 4

Rewrite eqtn 3 explicit to z:

z = 14.45 – 4x                     --> eqtn 5

Plug in the values of y (eqtn 4) and z (eqtn 5) to eqtn 2:

7 x + 2 (10.96 – 3 x) + 14.45 – 4 x = 30.40

7 x + 21.92 – 6 x + 14.45 – 4 x = 30.40

- 3 x + 36.37 = 30.40

- 3 x = - 5.97

x = 1.99

Eqtn 4:

y = 10.96 – 3 x   

y = 10.96 – 3 (1.99)

y = 4.99

Eqtn 5:

z = 14.45 – 4x

z = 14.45 – 4 (1.99)

z = 6.49

Therefore each shirt cost $1.99, each slacks cost $4.99, and each sports coat cost $6.49.