Question

task #1
at mikey moo’s ice cream shop, ice cream cones cost $1.10 and sundaes cost $2.35. one day, the receipts for a total of 172 cones and sundaes were $294.20.
how many ice cream cones were sold?
solve the system of equations using any method. answer the question in a complete sentence.

task #3
sasha earns $10.50 per hour at her job. she deposits everything she earns into her savings account. she currently has $150 in her savings account. jack earns $9.00 per hour at his job. he deposits everything he earns into his savings account. he currently has $300 in his savings account.
how many hours will both sasha and jack have to work in order to have the same amount of money in their accounts?

Explanation:

Task #1

Step1: Define variables and first equation (quantity)

Let \( x \) be the number of ice cream cones, \( y \) be the number of sundaes. Total number of cones and sundaes is 172, so \( x + y = 172 \).

Step2: Second equation (cost)

Cost of cones: \( 1.10x \), cost of sundaes: \( 2.35y \), total cost is \( 294.20 \), so \( 1.10x + 2.35y = 294.20 \).

Step3: Solve the system (using substitution or elimination)

From first equation, \( y = 172 - x \). Substitute into second equation:
\( 1.10x + 2.35(172 - x) = 294.20 \)
\( 1.10x + 404.2 - 2.35x = 294.20 \)
\( -1.25x = 294.20 - 404.2 \)
\( -1.25x = -110 \)
\( x = \frac{-110}{-1.25} = 88 \).

Step1: Define variables and equations

Let \( x \) be hours worked, \( y \) be total savings.
Sasha’s savings: \( y = 10.50x + 150 \)
Jack’s savings: \( y = 9.00x + 300 \)

Step2: Set equations equal (same savings)

\( 10.50x + 150 = 9.00x + 300 \)
\( 10.50x - 9.00x = 300 - 150 \)
\( 1.50x = 150 \)
\( x = \frac{150}{1.50} = 100 \).

Answer:

88 ice cream cones were sold.

Task #3