a:b=3:5; b:c=1:2 và a+b+c=180
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1 What is your hobby?
2 When did you start your hobby
3 Why do you enjoy your hobby
4 How many hours a day do you spend on your hobby
5 What does Jim usually do in his free time
6 How often does he play volleyball
7 Where does he often play volleyball
8 Who does he like to play volleyball with
I. Write questions for the underlined parts.
1. A: What is your hobby
B: My hobby is photography.
2. A:When did you started yor hobby
B: I started my hobby five years ago.
3. A:why do you enjoy your hobby
B: I enjoy my hobby because I think it’s creative.
4. A:How many hours a day fo you spend on your hobby
B: I spend two hours a day on my hobby.
5. A:What does Jim ussually do in his free time
B: Jim usually plays volleyball in his free time.
6. A:How often does he play volleyball
B: He plays volleyball three times a week.
7. A:Where does he often play volleyball
B: He often plays volleyball at the court near his school.
8. A:Who does he like to play with
B: He likes to play volleyball with his friends.
\(\frac{a}{3}=\frac{b}{5}=\frac{3a}{9}=\frac{b}{5}=\frac{3a-b}{9-5}=\frac{17,2}{4}=4,3\)
\(\frac{a}{3}=4\Rightarrow a=12,9\)
\(\frac{b}{5}=4,3\Rightarrow b=21,5\)
a+b=12.9+21.5=34.4
\(\frac{a}{b}=\frac{3}{5}\Rightarrow\frac{a}{3}=\frac{b}{5}=\frac{3a}{9}=\frac{b}{5}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\frac{3a}{9}=\frac{b}{5}=\frac{3a-b}{9-5}=\frac{17,2}{4}=4,3\)
\(\frac{a}{3}=4,3\Rightarrow a=4,3.3=12,9\)
\(\frac{b}{5}=4,3\Rightarrow b=21,5\)
\(\Rightarrow a+b=12,9+21,5=34,3\)
có a:b=3:5
'=>\(\frac{a}{3}\)=\(\frac{b}{5}\)
=>\(\frac{3a}{9}\)=\(\frac{b}{5}\)
Áp dụng tính chất dãy tỉ số bằng nhau
\(\frac{3a}{9}\)=\(\frac{b}{5}\)=\(\frac{3a-b}{9-5}\)=\(\frac{17.2}{4}\)=4.3
\(\frac{3a}{9}\)=4.3=>3a=38.7=>a=12.9
\(\frac{b}{5}\)=4.3=>b=21.5
=>a+b=12.9+21.5=34.4
Ta có : a : b = 3 : 5
=> a/3 = b/5
Áp dụng tính chất dãy tỉ số bằng nhau :
a/3 = b/5 = ( b - a) / ( 5 - 3 ) = -16/2 = -8
=> a = -21
b = -40
a:b=3:5
\(\Rightarrow\frac{a}{3}=\frac{b}{5}\) và 3a-b=17,2
Theo tính chất của dãy tỉ số bằng nhau, ta có:
\(\frac{a}{3}=\frac{b}{5}=\frac{a-b}{3-5}=\frac{3a-b}{3.3-5}=\frac{17,2}{4}=4,3\)
suy ra:
\(\frac{a}{3}=4,3\Rightarrow a=4,3.3=12,9\)
\(\frac{b}{5}=4,3\Rightarrow b=4,3.5=21,5\)
khi đó a+b=12,9+21,5=34,4
a:b đc 5 dư 3 => a= 5b+3
=> 5b= a-3
=> b/(a-3) = 1/5
vậy tỉ số là 1/5
Ta có : a:c được 5 và dư 3
Nên :a=5b+3
Hay :5b=a-3
Suy ra : \(\frac{b}{a-3}=\frac{1}{5}\)
Vậy tỉ số của b và a-3 là :\(\frac{1}{5}\)
- Xét: a : b = 9 : 4 \(\Rightarrow\frac{a}{9}=\frac{b}{4}\)\(\Rightarrow\frac{a}{45}=\frac{b}{20}\)
b : c = 5 : 3 \(\Rightarrow\frac{b}{5}=\frac{c}{3}\)\(\Rightarrow\frac{b}{20}=\frac{c}{12}\)
=> \(\frac{a}{45}=\frac{b}{20}=\frac{c}{12}\)
- Đặt: \(\frac{a}{45}=\frac{b}{20}=\frac{c}{12}=k\Rightarrow\hept{\begin{cases}a=45.k\\b=20.k\\c=12.k\end{cases}}\)
-Thay a = 45.k, b = 20.k , c = 12.k vào \(\frac{a-b}{b-c}\) ;ta có:
\(\frac{a-b}{b-c}=\frac{45.k-20.k}{20.k-12.k}=\frac{25.k}{8.k}=\frac{25}{8}\)
Vậy \(\frac{a-b}{b-c}=\frac{25}{8}\)
Ta có a:b=3:5=> \(\frac{a}{3}=\frac{b}{5}\left(1\right)\)
Lại có b:c=1:2=>\(\frac{b}{1}=\frac{c}{2}=>\frac{b}{5}=\frac{c}{10}\left(2\right)\)
Từ (1) và (2) => \(\frac{a}{3}=\frac{b}{5}=\frac{c}{10}=\frac{a+b+c}{3+5+10}=\frac{180}{18}=10\)
=> \(\hept{\begin{cases}a=30\\b=50\\c=100\end{cases}}\)
a : b = 3 : 5
=> a = \(\frac{3}{5}b\)
b : c = 1 ; 2
=> c = \(2b\)
Mà a + b + c = 180
=> \(\frac{3}{5}b\)+ b + 2b = 180
=> \(\left(\frac{3}{5}+1+2\right)b=180\)
=> \(\frac{18}{5}b=180\)
=> \(b=50\)
=> a = \(\frac{3}{5}b=\frac{3}{5}.50=30\)
c = 2b = 2 . 50 = 100
Vậy a = 30 ; b = 50 ; c = 100