Section 2.2 Introduction to Applications 67 1c. Aidan saves nickels and dimes in a jar. He has 20 more nickels than dimes and his collection is worth $8.50. Find the number of nickels and dimes in his collection. Solution 1c. What is unknown? The number of nickels and dimes is unknown. Let d represent the number of dimes. Then d + 20 represents the number of nickels. r 20 more nickels than dimes What is given? Together, the nickels and dimes are worth $8.50. Recall that dimes are each worth $0.10 and nickels are each worth $0.05. Value of dimes plus value of nickels is $8.50. 0.10d + 0.05(d + 20) = 8.50 Express the relationship. 0.10d + 0.05d + 1 = 8.50 Apply the distributive property. 0.15d + 1 = 8.50 Combine like terms. 0.15d + 1 - 1 = 8.50 - 1 Subtract 1 from each side. 0.15d = 7.50 Simplify. 0.15d 7.50 = 0.15 0.15 Divide each side by 0.15. d = 50 Simplify. Check: 0.10d + 0.05(d + 20) = 8.50 Begin with the original equation. 0.10(50) + 0.05(50 + 20) = 8.50 Replace d with 50. 5 + 0.05(70) = 8.50 Multiply and add inside parentheses. 5 + 3.5 = 8.50 Simplify. 8.50 = 8.50 True So, 50 is the solution of the equation and d + 20 = 50 + 20 = 70. Therefore, Aidan has 70 nickels and 50 dimes in his collection. 1d. Carrie invests $6000 in two accounts. If the amount she invests in the second account is $300 more than twice the amount invested in the first account, how much does Carrie invest in each account. Solution 1d. What is unknown? The amount of money invested in each account is unknown. Let f represent the amount invested in the first account. Then, 2 f + 300 represents the amount in the second account. What is given? Carrie invested $6000 in the two accounts. Amount invested plus amount invested is $6000. in first account in second account f + 2 f + 300 = 6000 Express the relationship. 3 f + 300 = 6000 Combine like terms. 3f + 300 - 300 = 6000 - 300 Subtract 300 from each side. 3f = 5700 Simplify. 3f 5700 = 3 3 Divide each side by 3. f = 1900 Simplify. s Twice the amount 300 more of the first account
hendricks_intermediate_algebra_1e_ch1_3
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