s. The couch wants to spend three-eighths of basketball practice time on defense. He plans to spend 45 min . on this. How mary hours will the team spend practicing? 4. Max Bui spent twice as much money as Alice on their shopping trip. If they spent a total of $$ \$ 386.16 $$, how much did each spend? Tit. Nr Jortem plans to leave the total of his savings to his four children. If they all are to receive the same amount of inhertunce and the total savings that he has is $$ \$ 501,052.40 $$, how much will each of them receive? 1. Exercises chocsea variable to represent the unknown. Write an equation and solve. 11. A recipe calls for $$ 2 \frac{1}{2} $$ cups of sugar. Maddie has only $$ 1 \frac{2}{3} $$ cups of sugar. How much more sugar does she need? I2 A Clristian university found that about $$ 3 \% $$ of its students came from a certain state. The university had 156 students from that state. What is the total enrollment in the university? is. Bub worked $$ 1 \frac{3}{4} $$ hr. longer on Tuesday than he did on Monday. He worked a total of $$ 13 \frac{1}{4} \mathrm{hr} $$. for the two dens. How many hours did he work on Monday? on Tuesday? 14. A music teacher needed 0.25 hr . per student to administer an oral test. If the teacher spent 3.75 hr . administering the test, how many students were tested? 15. The cost of a reserved seat is $$ 1 \frac{3}{4} $$ times the cost of general admission. If a reserved seat is $$ \$ 14 $$, what is the price of general admission? 16. Mrs. Harris made a quilt for her granddaughter. She used a total of $$ 7 \frac{7}{8} \mathrm{yd} $$. of material. If she used $$ 2 \frac{3}{4} $$ yd. of light blue material and $$ 3 \frac{5}{8} $$ yd. of dark blue, and the remaining material was a red print, how

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UpStudy AI · Accepted Answer

**1. Basketball Practice Time**

Let the total practice time be $$ T $$ (in minutes). According to the problem,
$$
\frac{3}{8}T = 45.
$$
Solve for $$ T $$:
$$
T = 45 \times \frac{8}{3} = 45 \times \frac{8}{3} = 120 \text{ minutes}.
$$
Convert minutes to hours:
$$
120 \text{ minutes} = \frac{120}{60} = 2 \text{ hours}.
$$

---

**2. Max Bui and Alice's Spending**

Let Alice spend $$ x $$ dollars. Then Max spends $$ 2x $$ dollars. The total spent is
$$
x + 2x = 386.16.
$$
Combine like terms:
$$
3x = 386.16,
$$
$$
x = \frac{386.16}{3} = 128.72.
$$
Thus, Alice spent $$ \$128.72 $$ and Max spent
$$
2x = 2(128.72) = 257.44.
$$

---

**3. Inheritance Distribution**

Let the amount each child receives be $$ x $$. There are 4 children and the total savings are
$$
4x = 501052.40.
$$
Solve for $$ x $$:
$$
x = \frac{501052.40}{4} = 125263.10.
$$

---

**4. Additional Sugar Needed**

Maddie has $$ 1\frac{2}{3} $$ cups and the recipe calls for $$ 2\frac{1}{2} $$ cups. Let $$ x $$ be the additional sugar needed.
$$
1\frac{2}{3} + x = 2\frac{1}{2}.
$$
Convert mixed numbers to improper fractions:
$$
1\frac{2}{3} = \frac{5}{3}, \quad 2\frac{1}{2} = \frac{5}{2}.
$$
Now,
$$
x = \frac{5}{2} - \frac{5}{3}.
$$
Find a common denominator (6):
$$
\frac{5}{2} = \frac{15}{6}, \quad \frac{5}{3} = \frac{10}{6},
$$
$$
x = \frac{15}{6} - \frac{10}{6} = \frac{5}{6}.
$$

---

**5. University Enrollment**

Let the total enrollment be $$ T $$. Given that $$ 3\% $$ of $$ T $$ equals 156,
$$
0.03T = 156.
$$
Solve for $$ T $$:
$$
T = \frac{156}{0.03} = 5200.
$$

---

**6. Bub's Work Hours**

Let the number of hours Bub worked on Monday be $$ m $$. Then on Tuesday he worked
$$
m + 1\frac{3}{4}.
$$
Express $$1\frac{3}{4}$$ as an improper fraction:
$$
1\frac{3}{4} = \frac{7}{4}.
$$
The total hours for both days is $$ 13\frac{1}{4} $$, which as an improper fraction is:
$$
13\frac{1}{4} = \frac{53}{4}.
$$
Set up the equation:
$$
m + \left(m + \frac{7}{4}\right) = \frac{53}{4}.
$$
Combine like terms:
$$
2m + \frac{7}{4} = \frac{53}{4},
$$
$$
2m = \frac{53}{4} - \frac{7}{4} = \frac{46}{4},
$$
$$
m = \frac{46}{8} = \frac{23}{4} \text{ hours}.
$$
Then Tuesday's hours are:
$$
m + \frac{7}{4} = \frac{23}{4} + \frac{7}{4} = \frac{30}{4} = \frac{15}{2} \text{ hours}.
$$

---

**7. Music Teacher's Testing Time**

The teacher spends $$ 0.25 $$ hours per student. With a total of $$ 3.75 $$ hours,
$$
\text{Number of students} = \frac{3.75}{0.25} = 15.
$$

---

**8. Reserved Seat Pricing**

Let the price of general admission be $$ G $$. The reserved seat costs
$$
1\frac{3}{4} \text{ times } G = \frac{7}{4} G.
$$
It is given that the reserved seat costs $$ \$14 $$:
$$
\frac{7}{4}G = 14.
$$
Solve for $$ G $$:
$$
G = 14 \times \frac{4}{7} = 8.
$$

---

**9. Quilt Material**

Mrs. Harris used a total of $$ 7\frac{7}{8} $$ yards of material. First, convert to an improper fraction:
$$
7\frac{7}{8} = \frac{63}{8} \text{ yards}.
$$
Light blue material used is $$ 2\frac{3}{4} $$:
$$
2\frac{3}{4} = \frac{11}{4} = \frac{22}{8} \text{ yards}.
$$
Dark blue material used is $$ 3\frac{5}{8} $$:
$$
3\frac{5}{8} = \frac{29}{8} \text{ yards}.
$$
Total used for light blue and dark blue is:
$$
\frac{22}{8} + \frac{29}{8} = \frac{51}{8}.
$$
The remaining material (red print) is:
$$
\frac{63}{8} - \frac{51}{8} = \frac{12}{8} = \frac{3}{2} \text{ yards}.
$$
1. **Basketball Practice Time**: The team will spend **2 hours** practicing. 2. **Max Bui and Alice's Spending**: - **Alice**: \$128.72 - **Max**: \$257.44 3. **Inheritance Distribution**: Each child will receive **\$125,263.10**. 4. **Additional Sugar Needed**: Maddie needs an additional **5⁄6 cup** of sugar. 5. **University Enrollment**: The total enrollment is **5,200 students**. 6. **Bub's Work Hours**: - **Monday**: 23⁄4 hours - **Tuesday**: 15⁄2 hours 7. **Music Teacher's Testing Time**: There are **15 students**. 8. **Reserved Seat Pricing**: General admission costs **\$8**. 9. **Quilt Material**: - **Red Print**: 3⁄2 yards

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