# Solutions

Great job on today’s word problem! Are you ready to check your answer? Look below to see if your solution matches ours.

**Lower Elementary:***Answer:* $3.90*Solution:* Zachary earned 15¢, 6 times for the books. That’s 15, 30, 45, 60, 75, 90¢ for all 6 of the books. He earned $1.00, 3 times for the toys. That’s $3.00 for all 3 of the toys. So, altogether, Zachary earned $0.90 + $3.00 = $3.90.

**Upper Elementary:***Answer:* 8:35 p.m.*Solution:* The amount of time it takes for all of the students to finish their songs is 8 × 5 = 40 minutes. Since they have to finish the recital by 9:15 p.m., we count back 40 minutes before 9:15 p.m. to 8:35 p.m.

**Middle School:***Answer:* 6 inches*Solution:* The length of the tree’s shadow is two-thirds the height of the tree. So, the length of the songbird’s shadow is two-thirds its height; 2 inches is two-thirds of 3 inches, so the songbird must be 3 inches tall. That means that the squirrel is 6 inches tall because 6 inches is twice as tall as 3 inches.

**Algebra and Up:***Answer:* They earned $0 in April.*Solution:* This function is a parabola that opens upward, so the lowest value is at the vertex. To find the month, we find –^{b }*⁄*_{2a}* *= – ^{–8} ⁄_{2(1)} = ^{8}⁄_{2} = 4. So the vertex is at *t *= 4, which represents the month of April. To find how much they earned, we set *t *= 4 and solve: 4^{2} – 8(4) + 16 = 16 – 32 + 16 = 0. So, the cat-sitting business earned $0 in April.