SOLUTION: Anna and Raj have some pens. Anna has 3 fewer pens than Raj. If Raj had 2 more pens, then he would have twice as many pens as Anna. How many pens do Anna and Raj have altogether?

Algebra ->  Equations -> SOLUTION: Anna and Raj have some pens. Anna has 3 fewer pens than Raj. If Raj had 2 more pens, then he would have twice as many pens as Anna. How many pens do Anna and Raj have altogether?      Log On


   

Question 982931: Anna and Raj have some pens. Anna has 3 fewer pens than Raj. If Raj had 2 more pens, then he would have twice as many pens as Anna. How many pens do Anna and Raj have altogether?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of pens Anna has
Let +r+ = number of pens Raj has
-----------------------------------
(1) +a+=+r+-+3+
(2) +r+%2B+2+=+2a+
-----------------
Substitute (1) into (2)
(2) +r+%2B+2+=+2%2A%28+r-3+%29+
(2) +r+%2B+2+=+2r+-+6+
(2) +r+=+8+
and
(1) +a+=+r+-+3+
(1) +a+=+8+-+3+
(1) +a+=+5+
-----------------
Together they have:
+a+%2B+r+=+5+%2B+8+=+13+
13 pens