Mike bought two types of pens: blue pens that cost $0.30 each and red pens that each cost \(d\) times as much as the blue pen. If the cost of 4 blue pens and 5 red pens was $3.45, what is the value of \(d\) ?

Summary Submit

We can write an equation for the total cost of the pens and the relationship between the pens:

$$ r = d(0.30) \scriptsize \tag*{\scriptsize relationship of price}$$ $$ 4(0.30)+5r=3.45 \scriptsize \tag*{\scriptsize total price}$$

We can solve the second equation directly.

$$ 4(0.30)+5r=3.45$$ $$ 1.2+5r=3.45 $$ $$ r=0.45 $$

Substitue this value into the first equation.

$$ r=d(0.30) $$ $$ 0.45 = d(0.30) $$ $$ d=\frac{45}{30} $$ $$ d=\boxed{1.5} $$