# investment question

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?

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1. 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 =(L+300)(I+0.02)
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.

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2. 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.

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