Question

1. you have some baseball trading cards. you give 21 baseball cards to a friend and have 9 left for yourself. how many baseball cards were in your original deck? write and solve an equation to find t, the number of baseball cards in your original deck.
2. model with math joy added 26 new contacts to her phone list. she now has a total of 100 contacts. let c represent how many contacts joy had on her phone list before she updated it. write an equation and solve for c.
3. reasoning jeremy bought a sandwich and a drink that cost him $7. his drink cost $1.75. solve the equation 7 = 5 + 1.75 to find s, the cost of jeremy’s sandwich.

Explanation:

Problem 17 (Baseball Cards)

Step1: Define the equation

Let \( t \) be the original number of cards. We gave 21 cards to a friend and have 9 left. So the equation is \( t - 21 = 9 \).

Step2: Solve for \( t \)

Add 21 to both sides of the equation: \( t - 21 + 21 = 9 + 21 \).
Simplify: \( t = 30 \).

Step1: Define the equation

Let \( c \) be the number of contacts before updating. Joy added 26 new contacts and now has 100. So the equation is \( c + 26 = 100 \).

Step2: Solve for \( c \)

Subtract 26 from both sides: \( c + 26 - 26 = 100 - 26 \).
Simplify: \( c = 74 \).

Step1: Define the equation

The equation is \( 7 = 5 + 1.75 \) (wait, actually, the correct equation from context: Let \( s \) be the cost of the sandwich. The total cost of sandwich and drink is 7, drink is 1.75, so \( s + 1.75 = 7 \)? Wait, the given equation is \( 7 = 5 + 1.75 \)? No, re-reading: "Jeremy bought a sandwich and a drink that cost him $7. His drink cost $1.75. He used the equation \( 7 = s + 1.75 \) to find \( s \), the cost of Jeremy’s sandwich." Wait, the user wrote "the equation 7 = 5 + 1.75" – maybe a typo, should be \( 7 = s + 1.75 \). Let's solve that.

Step1: Solve for \( s \)

Subtract 1.75 from both sides: \( 7 - 1.75 = s + 1.75 - 1.75 \).
Simplify: \( 5.25 = s \).
Wait, but the user wrote "the equation 7 = 5 + 1.75" – if that's the equation, then \( 5 + 1.75 = 6.75
eq 7 \), so maybe a typo. Assuming the correct equation is \( s + 1.75 = 7 \) (since total is 7, drink is 1.75, sandwich is \( s \)).
So solving \( s + 1.75 = 7 \):
Subtract 1.75: \( s = 7 - 1.75 = 5.25 \).

Answer:

The original number of baseball cards is \( \boldsymbol{30} \).

Problem 18 (Joy's Phone Contacts)