System of equations for buying stamps

You have 16 stamps.  Some are postcard stamps that cost $0.23, and the rest cost $0.41.  If you spend a total of $5.30 on the stamps, how many postcard stamps do you have?
A.)  7
B.)  8
C.)  9
D.)  10
E.)  cannot be determined

---

x = postcard stamps
y = other stamps

x + y = 16   {you have 16 total stamps}
0.23x + 0.41y = 5.3   {postcard stamps are $0.23 and others are $0.41}

-0.23x - 0.23y = -3.68   {multiplied top equation by -0.23}
0.23x + 0.41y = 5.3   {bottom equation stays the same}
---------------------------
         0.18y = 1.62   {added the two equations}
                y = 9   {divided each side by 0.18}

x + y = 16   {top original equation}
x + 9 = 16   {substituted 9, in for y, into top original equation}
x = 7   {subtracted 9 from each side}

A.)  7 postcard stamps

Ask Algebra House
​