62 Chapter 1 Linear Equations and Inequalities in One Variable To establish a mathematical model, we know that the total return ($625) must equal the earnings from the bond fund plus the earnings from the stock fund: 1Earnings from bond fund2 1earnings from stock fund2 1total earnings2 0.04x 0.07110,000 x2 625 0.04x 0.07(10,000 x) 625 Mathematical equation 4x 7(10,000 x) 62,500 Multiply by 100 to clear decimals. 4x 70,000 7x 62,500 3x 70,000 62,500 Combine like terms. The amount invested in the bond fund is $2500. The amount invested in the stock fund is $10,000 x, or $7500. Skill Practice 5. Jonathan borrowed $4000 in two loans. One loan charged 7% interest, and the other charged 1.5% interest. After 1 yr, Jonathan paid $225 in interest. Find the amount borrowed in each loan. 5. Applications Involving Mixtures Solving a Mixture Application How many liters (L) of a 40% antifreeze solution must be added to 4 L of a 10% antifreeze solution to produce a 35% antifreeze solution? Solution: The given information is illustrated in Figure 1-1. 40% Antifreeze solution 0.40x L of pure antifreeze x L of solution 3x7500 Subtract 70,000 from both sides. x 2500 Solve for x and interpret the results. 35% Antifreeze solution 0.35(4 x) L of pure antifreeze 10% Antifreeze solution 0.10(4) L of pure antifreeze 4 L of solution (4 x) L of solution Figure 1-1 Example 6 3x 3 7500 3 TIP: To understand the role of the concentration rate within a mixture problem, consider this example. Suppose you had 30 gal of a 10% antifreeze mixture. How much pure antifreeze is in the mixture? pure antifreeze 0.10(30 gal) 3 gal Multiply the concentration rate by the amount of mixture. Answer 5. $3000 was borrowed at 7% interest, and $1000 was borrowed at 1.5% interest.
miller_intermediate_algebra_4e_ch1_3
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