posted by Joe on .
scott and laura have both invested some money. Scott invested $3,000 more then laura and at a 2% higher interest rate. If scott received $800 annual interest and laura received $400, how much did scott invest?
Let their investments be L (Laura) and S (Scott). Laura's annual interest rate is I (expressed as a decimal) and Scott's is I + 0.02
S = L + 3000
800 = S*(I + 0.02)
400 = L I
You have three equations in three unknowns, which is enough to solve for all of them.
800 = LI + 300I +0.02L + 6
= 400 + 300I + 0.02L+ 6
= 400 + 300*400/L + 0.02L + 6
= 406 + 120000/L +0.02L
This can be turned into a quadratic equation for L. Take the positive root.
Actually, you should take the negative root. You should plug both answers into the original equation to see which one fits. The one that makes sense (i.e. 800=800) should be the correct one.
Don't forget that Scott invested 3,000 more than Sally (S = L + 3000). You just solved for L. The question is asking for what S is. You're not done yet.