Question

kiana buys 2 pounds of peaches and 3 pounds of blueberries to make her famous peach and blueberry pies. she spent a total of $18. let x equal the cost, per pound, of the peaches. the blueberries cost $0.50 less, per pound, than the peaches. part a: which equation models this situation? an equation to model this situation is 3x - 2(x + 0.5) = 18 an equation to model this situation is 2x + 3(x + 0.5) = 18 an equation to model this situation is 2x + 3(x - 0.5) = 18 an equation to model this situation is 2x + 3x = 18 - 0.5 part b: what is the cost of 1 pound of peaches? what is the cost of 1 pound of blueberries?

Explanation:

Step1: Identificar la ecuación correcta para el problema

Kiana compra 2 libras de duraznos a $x$ dólares el kilo y 3 libras de arándanos, donde el precio por libra de arándanos es $x - 0.5$ dólares. El total gastado es de $18$ dólares. El costo de los duraznos es $2x$ y el costo de los arándanos es $3(x - 0.5)$. La ecuación que modela la situación es $2x+3(x - 0.5)=18$.

Step2: Resolver la ecuación para $x$ (costo de 1 libra de duraznos)

Comenzamos expandiendo la ecuación:
$$2x+3x-1.5 = 18$$
Combinamos términos semejantes:
$$5x-1.5 = 18$$
Sumamos 1.5 a ambos lados:
$$5x=18 + 1.5$$
$$5x=19.5$$
Dividimos ambos lados por 5:
$$x=\frac{19.5}{5}=3.9$$

Step3: Encontrar el costo de 1 libra de arándanos

El costo de 1 libra de arándanos es $x - 0.5$. Sustituyendo $x = 3.9$, tenemos $3.9-0.5 = 3.4$

Answer:

Part A: An equation to model this situation is $2x + 3(x - 0.5)=18$
Part B: The cost of 1 pound of peaches is $3.9$ dólares.
The cost of 1 pound of blueberries is $3.4$ dólares.