Question

a small business sold a combination of premium widgets for $5 each and standard widgets for $2 each for a total of $26. the business sold a total of 10 premium and standard widgets. the equations that model this scenario are: p + s = 10, 5p + 2s = 26. where p represent the number of premium widgets and s represents the number of standard widgets. how many premium widgets were sold? 10 2 1 8

Explanation:

Step1: Isolate s from first - equation

From \(p + s=10\), we get \(s = 10 - p\).

Step2: Substitute s into second - equation

Substitute \(s = 10 - p\) into \(5p+2s = 26\). So \(5p+2(10 - p)=26\).

Step3: Expand and simplify

Expand \(5p+2(10 - p)\) to get \(5p + 20-2p=26\). Combine like - terms: \(3p+20 = 26\).

Step4: Solve for p

Subtract 20 from both sides: \(3p=26 - 20=6\). Then divide both sides by 3: \(p = 2\).

Answer:

2