Question

algebra 1 w/probability
study guide – proportions, equations in context, and inequalities
name:
date: 9 - 11 - 2025
period:
solve each proportion.

1. $\frac{2}{15}=\frac{x}{135}$
2. $\frac{2}{9}=\frac{4}{x + 8}$
3. $\frac{6}{a - 6}=\frac{3}{a - 3}$
4. your grandmother is making a birthday cake for you. the recipe calls for 3 eggs and 2 cups of flour. grandma wants to make an extra - large cake so it will feed the whole family. she is going to use 8 eggs. how many cups of flour should she use? use a proportion to solve the problem. write your answer in fraction form.

write an equation and solve.

1. as a part of their government class, maddie and ryan had to log volunteer hours in their community. ryan volunteered for one more than 3 times the number of hours that maddie did. all together they volunteered in their community for 45 hours. how many hours did each student volunteer?
2. the product of a number and three is equivalent to twice a number plus eight.

write an inequality and solve.

1. twice a number is greater than 10 less than the number.
2. ten plus a number is at most 3 times the number minus two.

Explanation:

1. Resolver la proporción $\frac{2}{15}=\frac{x}{135}$

Step1: Aplicar la propiedad de proporciones

$15x = 2\times135$

Step2: Calcular el lado derecho

$15x=270$

Step3: Despejar $x$

$x=\frac{270}{15}=18$

2. Resolver la proporción $\frac{2}{9}=\frac{4}{x + 8}$

Step1: Aplicar la propiedad de proporciones

$2(x + 8)=4\times9$

Step2: Expandir el lado izquierdo

$2x+16 = 36$

Step3: Restar 16 de ambos lados

$2x=36 - 16=20$

Step4: Dividir entre 2

$x = 10$

3. Resolver la proporción $\frac{6}{a - 6}=\frac{3}{a - 3}$

Step1: Aplicar la propiedad de proporciones

$6(a - 3)=3(a - 6)$

Step2: Expandir ambos lados

$6a-18 = 3a-18$

Step3: Restar $3a$ de ambos lados

$6a-3a-18=3a-3a - 18$
$3a-18=-18$

Step4: Sumar 18 a ambos lados

$3a=-18 + 18=0$

Step5: Dividir entre 3

$a = 0$

4. Resolver el problema de la receta

Answer:

1. $x = 18$
2. $x = 10$
3. $a = 0$
4. $\frac{16}{3}$ tazas de harina
5. Maddie: 11 horas, Ryan: 34 horas
6. $n = 8$
7. $n>-10$
8. $n\geqslant6$