Question

1. rick bought a total of 8 pounds of steak and chicken. if steak costs $13.50 per pound and chicken costs $3.25 per pound and he paid a total of $77.25, how many pounds of steak did he purchase?

variables:
solve:
system:
solution:

1. anna has a collection of 45 nickels and quarters worth $8.05. how many nickels does she have?

variables:
solve:
system:
solution:
© gina wilson (all things algebra*, llc), 2016

Explanation:

Problem 6

Step1: Define variables

Let $x$ = pounds of steak, $y$ = pounds of chicken.

Step2: Set up system of equations

Total weight: $x + y = 8$
Total cost: $13.50x + 3.25y = 77.25$

Step3: Isolate $y$ from first equation

$y = 8 - x$

Step4: Substitute into cost equation

$13.50x + 3.25(8 - x) = 77.25$

Step5: Simplify and solve for $x$

$13.50x + 26 - 3.25x = 77.25$
$10.25x = 77.25 - 26$
$10.25x = 51.25$
$x = \frac{51.25}{10.25} = 5$

Step1: Define variables

Let $n$ = number of nickels, $q$ = number of quarters.

Step2: Set up system of equations

Total coins: $n + q = 45$
Total value (in cents): $5n + 25q = 805$

Step3: Isolate $q$ from first equation

$q = 45 - n$

Step4: Substitute into value equation

$5n + 25(45 - n) = 805$

Step5: Simplify and solve for $n$

$5n + 1125 - 25n = 805$
$-20n = 805 - 1125$
$-20n = -320$
$n = \frac{-320}{-20} = 16$

Answer:

5 pounds

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Problem 7