Question

1. lily and her children went into a grocery store and she bought $7 worth of apples and bananas. each apple costs $1 and each banana costs $0.50. she bought 5 times as many bananas as apples. by following the steps below, determine the number of apples, $x$, and the number of bananas, $y$, that lily bought.

determine three ways to have 5 times as many bananas as apples:
(apples, bananas) = (1, 5)
(apples, bananas) = (2, 10)
(apples, bananas) = (3, 15)
on the graph below, plot the three points as if they were coordinate pairs. then draw a line through the points.
determine three ways to have a total cost of $7:
(apples, bananas) = (1, 12)
(apples, bananas) = (3, 8)
(apples, bananas) = (5, 4)
on the graph below, plot the three points as if they were coordinate pairs. then use them to draw a second line.
use the graph to answer the question:
lily bought __ apples and __ bananas.

Explanation:

Step1: Define variables and equations

Let $x$ = number of apples, $y$ = number of bananas.

1. Relationship: $y = 5x$
2. Cost equation: $1x + 0.5y = 7$

Step2: Substitute $y$ into cost equation

Substitute $y=5x$ into $x + 0.5y = 7$:
$x + 0.5(5x) = 7$

Step3: Simplify and solve for $x$

Calculate and combine like terms:
$x + 2.5x = 7$
$3.5x = 7$
$x = \frac{7}{3.5} = 2$

Step4: Solve for $y$

Use $y=5x$:
$y = 5(2) = 10$

Answer:

Lily bought 2 apples and 10 bananas.