Algebra Word Problem, Please Help!!?
Can someone please explain how you solve this problem?
Simone earned $500 doing extra chores during the summer. She put some of the money in a CD that earned 5.5%. She put twice as much in a savings account that earned 4.8%. She put the same amount that she put in the savings account into a bond fund that earned 3.7%. After one year, the three accounts made $22.50 in interest. How much did Simone put in the CD?
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Let C be the amount of money she put in the CD
S = the amount of money in the savings account = 2C
B = the amount of money in the Bond account = S = 2C
The amount of interest an account earns in a year is given by r* X where r is the interest rate and X is the amount o money in a particular account. Let
r_cd be the cd interest rate
r_s be the savings interest rate
r_b be the bond interest rate
The total interest earned is then:
C * r_cd + S * r_s + B * r_b
substituting S and B in terms of C gives:
C * r_cd + 2C * r_s + 2C * r_b = Interest Earned
factor C
C (r_cd + 2 * r_s + 2 * r_b) = Interest Earned
C = Interest Earned / (r_cd + 2 * r_s + 2 * r_b)
C = 22.50 / (0.055 + 2 * 0.048 + 2 * 0.037)
C = $100
You can say x+2x+2x=500
So x =100 = amount in CD