Question

homework
circle the number of the problem that is not a proportion
problem. solve each proportion problem.

1. ( 3:5::21:r )

( r=)

1. ( b:7::16:56 )

( b=)

1. what is the basic ratio for ( 30:42 )?
2. the basic ratio for ( 36:84 ) is
3. what is the basic ratio for ( 5:15 )?
4. in the zoo, there are 6 flamingos for
5. josh and sally each bike at their own

every 8 ducks. if there are 20 ducks,
constant rates. josh bikes 35 miles

how many flamingos are there?
while sally bikes 40 miles. if sally bikes
16 miles, how far does josh bike?

1. alice is delivering mail on maple
2. ( 9:24::24:d )

street. she has letters for house
( d=)
#4 and #6. if she has letters for #20,
what other house does she have
letters for?

Explanation:

Step1: Resolver la proporción \(3:5::21:r\)

En una proporción \(a:b::c:d\), se cumple \(a\times d = b\times c\). Entonces, \(3\times r=5\times21\), es decir \(3r = 105\). Dividiendo ambos lados por 3: \(r=\frac{105}{3}=35\).

Step2: Resolver la proporción \(b:7::16:56\)

Usando la regla \(a\times d = b\times c\), tenemos \(b\times56 = 7\times16\). Entonces \(56b=112\). Dividiendo por 56: \(b = \frac{112}{56}=2\).

Step3: Encontrar la razón básica de \(30:42\)

Dividir numerador y denominador por su máximo común divisor. El MCD de 30 y 42 es 6. Entonces \(\frac{30\div6}{42\div6}=\frac{5}{7}\).

Step4: Encontrar la razón básica de \(36:84\)

El MCD de 36 y 84 es 12. Entonces \(\frac{36\div12}{84\div12}=\frac{3}{7}\).

Step5: Encontrar la razón básica de \(5:15\)

El MCD de 5 y 15 es 5. Entonces \(\frac{5\div5}{15\div5}=\frac{1}{3}\).

Step6: Resolver el problema de los flamencos y patos

La proporción es \(6:8 = x:20\). Usando \(a\times d = b\times c\), \(8x=6\times20\), \(8x = 120\), \(x=\frac{120}{8}=15\).

Step7: Resolver el problema de Josh y Sally

La proporción es \(35:40 = y:16\). Usando \(a\times d = b\times c\), \(40y=35\times16\), \(40y = 560\), \(y=\frac{560}{40}=14\).

Step8: Resolver el problema de Alice

Las casas \(4\) y \(6\) tienen una relación \(4:6 = 2:3\). Si la casa es \(20\), \(2:3=20:z\). Usando \(a\times d = b\times c\), \(2z=3\times20\), \(2z = 60\), \(z = 30\).

Step9: Resolver la proporción \(9:24::24:d\)

Usando \(a\times d = b\times c\), \(9\times d=24\times24\), \(9d = 576\). Dividiendo por 9: \(d=\frac{576}{9}=64\).

Answer:

1. \(r = 35\)
2. \(b = 2\)
3. \(\frac{5}{7}\)
4. \(\frac{3}{7}\)
5. \(\frac{1}{3}\)
6. \(15\) flamencos
7. \(14\) millas
8. Casa \#30
9. \(d = 64\)