Question

there are 88 seats in a theater. the seating in the theater is split into 4 identical sections. each section has 14 red seats and some blue seats.
a. complete the description of a tape diagram that can represent the situation.
a tape diagram with ____ equal parts, each labeled $x + 14$, for a total of ____.
b. find the unknown amounts that can be found by using the diagram or reasoning about the situation.
number of seats per section: ______
number of blue seats per section: ______
total number of red seats in the theater: ______
total number of blue seats in the theater: ______

Explanation:

Step1: Fill tape diagram blanks

The theater has 4 identical sections, so the first blank is 4. Total seats are 88, so the second blank is 88.

Step2: Calculate seats per section

Divide total seats by sections:
$\frac{88}{4}=22$

Step3: Find blue seats per section

Subtract red seats per section from total per section:
$22 - 14 = 8$

Step4: Calculate total red seats

Multiply red seats per section by sections:
$14 \times 4 = 56$

Step5: Calculate total blue seats

Multiply blue seats per section by sections:
$8 \times 4 = 32$

Answer:

a. A tape diagram with $\boldsymbol{4}$ equal parts, each labeled $x + 14$, for a total of $\boldsymbol{88}$.
b.
number of seats per section: $\boldsymbol{22}$
number of blue seats per section: $\boldsymbol{8}$
total number of red seats in the theater: $\boldsymbol{56}$
total number of blue seats in the theater: $\boldsymbol{32}$