Question

john spends $94 to buy packages of cleaning supplies for a camp. he buys ( t ) packages of towels; each package is $5 and contains 8 towels. he also buys ( s ) packages of soap; each package is $4 and contains 10 bars of soap. john buys 20 packages of cleaning supplies altogether.
a. write a system of two equations to represent the packages of cleaning supplies john buys.
b. how many packages of towels does john buy?

Explanation:

Step1: Define variables

Let $t$ = number of towel packages, $s$ = number of soap packages.

Step2: Total packages equation

Total packages equal 20:
$t + s = 20$

Step3: Total cost equation

Cost of towels + soap = $94$:
$5t + 4s = 94$

Step4: Solve the system (substitution)

From Step2: $s = 20 - t$. Substitute into cost equation:
$5t + 4(20 - t) = 94$

Step5: Simplify and solve for $t$

$5t + 80 - 4t = 94$
$t + 80 = 94$
$t = 94 - 80 = 14$

Answer:

A. The system of equations is:
$t + s = 20$
$5t + 4s = 94$
B. 14