Soumik has $5 less than his friend Kofi. If they have $97.50 altogether, how much does each person have?

Wednesday, July 20, 2016

Soumik has $5 less than his friend Kofi. If they have $97.50 altogether, how much does each person have?

Hello!

The most clear method to solve this is to denote the variables and to solve the system of equations that occurs. This system is simple!

Let $\displaystyle{S}$ be the amount of dollars Soumik have, and $\displaystyle{K}$ that Kofi have. "Soumik has $\displaystyle\${5}$ less than his friend Kofi" gives us the equation

$\displaystyle{S}={K}-{5},$

and "they have $\displaystyle\${97.50}$ altogether" gives the equation

$\displaystyle{S}+{K}={97.50}.$

Substitute $\displaystyle{S}$ from the first equation to the second and get

$\displaystyle{K}-{5}+{K}={97.50},$ thus $\displaystyle{2}{K}={97.50}+{5}={102.50},$

and finally $\displaystyle{K}=\frac{{102.50}}{{2}}={51.25}{\left(\$\right)}.$

Recall that $\displaystyle{S}={K}-{5}$ and find $\displaystyle{S}={51.25}-{5}={46.25}{\left(\$\right)}.$

The answer: Soumik has $46.25 and Kofi has $51.25.

Ninenotes

Wednesday, July 20, 2016

Soumik has $5 less than his friend Kofi. If they have $97.50 altogether, how much does each person have?

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