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.

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