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A. Solve N in each equation and then check the results.
1.) 2 (N + 4) = 5
2.) [tex]\frac{(N - 5)}{4}[/tex] = 7

B. Write an equivalent algebraic equation for each situation. Then, solve the equation.
1. Tina brought a basket of 28 fruits to the home for the aged. The basket had pineapples and oranges. The oranges were 6 times more than the pineapples. How many of each kind of fruit did she bring?
2. Marla weights half as much as her father who weighs 85 kg. How much does Marla weigh?
3. Meena is babysitting her friend's daughter, Noella, who is two years younger than her brother, Josef. The total age of Noella and Josef is 10 years. How old is Noella? How old is Josef?
4. In November and December, Agee and Jay volunteered to help at their public library. They volunteered for a total of 102 hours. Agee served 8 hours more than Jay did. How long did each work at the health center as volunteers?
5. On the table are 44 books on Science, History, and Geography. There are twice as many Science books as there are History books. There are 8 Geography books. How many Science books are there? How many are History books?

Sagot :

Dalbalatzov2vtoidn

Answer:

May mga ipapasa akong requirements bukas pero unahin ko muna ito haha.

A.

1.) Solution:

[tex]2(N + 4) = 5\\2N+8=5\\2N=5-8\\2N=-3\\\frac{2N}{2} =\frac{-3}{2} \\N= \frac{3}{2}[/tex]

Checking:

[tex]2(N + 4)=5\\2 (\frac{-3}{2} + 4) = 5\\2 (\frac{5}{2} ) = 5\\5=5[/tex]

2.) Solution:

[tex]\frac{(N-5)}{4} =7\\\frac{(N-5)}{4}(4) =7(4)\\\\(N-5)=28\\N=28+5\\N=33[/tex]

Checking:

[tex]\frac{(N-5)}{4} =7\\\frac{(33-5)}{4} =7\\\frac{(28)}{4} =7\\7=7[/tex]

B.

1. Let x be the number of pineapples.

[tex](x+6)+x=28\\x+x=28-6\\2x=22\\\frac{2x}{2}=\frac{22}{2}\\x=11[/tex]

To find the number of oranges:

[tex](x+6)\\(11+6)\\17[/tex]

Answer: There are 11 pineapples and 17 oranges.

2. Let w be Maria's weight.

[tex]2w=85\\\frac{2w}{2}=\frac{85}{2}\\w=42.5[/tex]

Answer: Maria weighs 42.5 kg.

3. Let a be the age of Josef.

[tex]a+(a-2)=10\\a+a=10+2\\2a=12\\\frac{2a}{2}=\frac{12}{2} \\a=6[/tex]

The age of Noella:

[tex](a-2)\\(6-2)\\4[/tex]

Answer: Josef is 6 years old, and Noella is 4 years old.

4. Let t be Jay's volunteer hours.

[tex]t+(t+8)=102\\t+t=102-8\\2t=94\\\frac{2t}{2}=\frac{94}{2} \\t=47[/tex]

To find Agee's volunteer hours:

[tex](t+8)\\(47+8)\\55[/tex]

Answer: Jay's volunteer hours are 47 hours, and Agee's volunteer hours are 55 hours.

5. Let b be the number of History books.

[tex]b+(2b)+8=44\\b+2b=44-8\\3b=36\\\frac{3b}{3} = \frac{36}{3}\\b=12[/tex]

To find the Science books:

[tex]2b\\2(12)\\24[/tex]

Answer: There are 12 History books and 24 Science books.