Question

The track team is trying to reduce their time for a relay race. First they reduce their time by 8 seconds. Then they are able to reduce that time by 25%. If their final time is 51 seconds, what was their beginning time?
Choose the tape diagram that represents the number of seconds in their second time.

x
Time 1

Time 2
x −8

x
Time 1

Time 2
8
x
Excellent!
Choose the tape diagram that represents their final time.

x
Time 1

Time 2
x −8
Time 3
51

x
Time 1

Time 2
x −8
Time 3
51
Good work!
Write an equation in words to represent this situation.
x
Time 1

Time 2
x −8
Time 3
51

125% of Time 2 = Time 3

50% of Time 2 = Time 3

25% of Time 2 = Time 3

75% of Time 2 = Time 3
Excellent!
Write an equation to represent this situation.
x
Time 1

Time 2
x −8
Time 3
51
75% of Time 2 = Time 3
You got it!
Solve the equation to find the value of x. You can show your work on Zearn or on paper, then enter your answer on Zearn.
0.75(x−8)
=
51

x
=
Good work!
What does x = 76 represent in this situation?

The track team reduced their time by 76 seconds.

The track team’s first time was 76 seconds.

The track team’s second time was 76 seconds.

Answer 1

In this situation, the value \( x = 76 \) represents the track team’s first time, which is 76 seconds.

To clarify the process:
- The team starts with a beginning time of \( x \) seconds.
- Then, they reduce their time by 8 seconds, resulting in their second time of \( x - 8 \) seconds.
- They further reduce this second time by 25%, giving their final time of 51 seconds.

Therefore, \( x \) represents the initial time before any reductions were made.