Explorations | CCTT MathSummer

Explorations

Solve Each Equation

1. ^y/₂ + ^y/₅ = 21 2. ^c/₃ - ^c/₇ = 12 3. ^2x/₃ + ⁵/₉ = ^x/₉

4. ³/₄k - 5 = ¹/₂k 5. ⁵/₆a + 2 = ⁹/₁₀a 6. ³/₄b - ⁷/₈ = ³/₂ b

7. ^2p/₅ + ³/₁₀ = ^p/₅ + 2 8. ^3t/₄ - ⁵/₆ = ^7t/₁₂ + ¹/₄ 9. ^5v/₇ - ¹/₂ = ^v/₂ - 4

Solve Each Equation

10. 2.5n - 4.3 = 8.7 11. 7.6 + 0.6w = 3.7

12. 5.2 - 0.5m = -1.8m 13. 4.3z = 0.05z - 34

14. -0.004r + 36 = 0.14r 15. 3v - 1.89 = 1.74v

16. 4x - 0.63 = 8x + 0.77 17. 9 + 2.8y = 1.6y - 3

18.

In a road test of a new car for the consumer magazine she works for, Garnetta drove to a preassigned location through city streets and came back via a highway. The car gets 24 mi/gal in the city and 30 mi/gal on the highway, and round trip used up 12 gal of gas. What distance did she drive each way?

19.

Hisako ran a cross-country race in which the course was divided into 3 equal legs. Hisako ran the first leg at 12 km/h and the last two legs at 16 km/h. The whole race took her 50 min. How long was each leg? How long was the entire course?

20.

Ricardo started a copying job on the newer of the two copiers in his office, which does 2- pages per minute. He finished 3 of 4 equal-sized stacks, before a rush job bumped him to the older copier, which does 10 pages per minute. There he did the last stack. The whole job took him 15 minutes. How many pages were in each stack?

21.
Writing Describe a way to find the least comon multiple of two given numbers. Include a way to decide when the least common multiple is equal to the product of the two numbers.

1. ^y/₂ + ^y/₅ = 21	2. ^c/₃ - ^c/₇ = 12	3. ^2x/₃ + ⁵/₉ = ^x/₉
4. ³/₄k - 5 = ¹/₂k	5. ⁵/₆a + 2 = ⁹/₁₀a	6. ³/₄b - ⁷/₈ = ³/₂ b
7. ^2p/₅ + ³/₁₀ = ^p/₅ + 2	8. ^3t/₄ - ⁵/₆ = ^7t/₁₂ + ¹/₄	9. ^5v/₇ - ¹/₂ = ^v/₂ - 4

10.	2.5n - 4.3 = 8.7	11.	7.6 + 0.6w = 3.7
12.	5.2 - 0.5m = -1.8m	13.	4.3z = 0.05z - 34
14.	-0.004r + 36 = 0.14r	15.	3v - 1.89 = 1.74v
16.	4x - 0.63 = 8x + 0.77	17.	9 + 2.8y = 1.6y - 3

18.	In a road test of a new car for the consumer magazine she works for, Garnetta drove to a preassigned location through city streets and came back via a highway. The car gets 24 mi/gal in the city and 30 mi/gal on the highway, and round trip used up 12 gal of gas. What distance did she drive each way?
19.	Hisako ran a cross-country race in which the course was divided into 3 equal legs. Hisako ran the first leg at 12 km/h and the last two legs at 16 km/h. The whole race took her 50 min. How long was each leg? How long was the entire course?
20.	Ricardo started a copying job on the newer of the two copiers in his office, which does 2- pages per minute. He finished 3 of 4 equal-sized stacks, before a rush job bumped him to the older copier, which does 10 pages per minute. There he did the last stack. The whole job took him 15 minutes. How many pages were in each stack?
21.	Writing Describe a way to find the least comon multiple of two given numbers. Include a way to decide when the least common multiple is equal to the product of the two numbers.