Word Problems 208207

1. **Problem:** Sarah earned 3 more than double Eric's earnings. The difference is 15. Find their earnings. 2. **Formula:** Let Eric's earnings be $x$. Then Sarah's earnings are $2x + 3$. The difference is $15$. 3. **Equation:** $ (2x + 3) - x = 15 $ 4. **Simplify:** $ 2x + 3 - x = 15 $ 5. **Combine like terms:** $ x + 3 = 15 $ 6. **Subtract 3:** $ x + \cancel{3} - \cancel{3} = 15 - 3 $ 7. **Result:** $ x = 12 $ 8. **Sarah's earnings:** $ 2(12) + 3 = 24 + 3 = 27 $ 9. **Answer:** Eric earned 12, Sarah earned 27. --- 1. **Problem:** Rectangle length is 2 cm less than 7 times width. Perimeter is 60 cm. Find width and length. 2. **Formula:** Let width be $w$, length $l = 7w - 2$. Perimeter $P = 2(l + w) = 60$ 3. **Equation:** $ 2((7w - 2) + w) = 60 $ 4. **Simplify:** $ 2(8w - 2) = 60 $ 5. **Distribute:** $ 16w - 4 = 60 $ 6. **Add 4:** $ 16w - 4 + 4 = 60 + 4 $ 7. **Result:** $ 16w = 64 $ 8. **Divide:** $ \frac{16w}{16} = \frac{64}{16} $ 9. **Result:** $ w = 4 $ 10. **Length:** $ l = 7(4) - 2 = 28 - 2 = 26 $ 11. **Answer:** Width is 4 cm, length is 26 cm. --- 1. **Problem:** Girls are 3 less than double boys. Total 30 students. Find number of boys and girls. 2. **Formula:** Let boys be $b$, girls $g = 2b - 3$. Total $b + g = 30$ 3. **Equation:** $ b + (2b - 3) = 30 $ 4. **Simplify:** $ 3b - 3 = 30 $ 5. **Add 3:** $ 3b = 33 $ 6. **Divide:** $ b = 11 $ 7. **Girls:** $ g = 2(11) - 3 = 22 - 3 = 19 $ 8. **Answer:** Boys 11, girls 19. --- 1. **Problem:** Michelle scored 5 more than triple Carolyn's score. Together 45 points. 2. **Formula:** Let Carolyn's score $c$, Michelle's $m = 3c + 5$. Total $m + c = 45$ 3. **Equation:** $ (3c + 5) + c = 45 $ 4. **Simplify:** $ 4c + 5 = 45 $ 5. **Subtract 5:** $ 4c = 40 $ 6. **Divide:** $ c = 10 $ 7. **Michelle:** $ m = 3(10) + 5 = 35 $ 8. **Answer:** Carolyn 10, Michelle 35. --- 1. **Problem:** Randy has dimes and quarters. Dimes are 16 more than triple quarters. Total 36 coins. 2. **Formula:** Let quarters $q$, dimes $d = 3q + 16$. Total $d + q = 36$ 3. **Equation:** $ (3q + 16) + q = 36 $ 4. **Simplify:** $ 4q + 16 = 36 $ 5. **Subtract 16:** $ 4q = 20 $ 6. **Divide:** $ q = 5 $ 7. **Dimes:** $ d = 3(5) + 16 = 31 $ 8. **Answer:** Quarters 5, dimes 31. --- 1. **Problem:** Rectangle length is 7 cm more than twice width. Perimeter 86 cm. 2. **Formula:** Width $w$, length $l = 2w + 7$, perimeter $2(l + w) = 86$ 3. **Equation:** $ 2((2w + 7) + w) = 86 $ 4. **Simplify:** $ 2(3w + 7) = 86 $ 5. **Distribute:** $ 6w + 14 = 86 $ 6. **Subtract 14:** $ 6w = 72 $ 7. **Divide:** $ w = 12 $ 8. **Length:** $ l = 2(12) + 7 = 31 $ 9. **Answer:** Width 12 cm, length 31 cm. --- 1. **Problem:** 27 coins in nickels and dimes total 2.15. Find number of each. 2. **Formula:** Nickels $n$, dimes $d$, $n + d = 27$, value $0.05n + 0.10d = 2.15$ 3. **Multiply value by 100:** $5n + 10d = 215$ 4. **From first:** $n = 27 - d$ 5. **Substitute:** $5(27 - d) + 10d = 215$ 6. **Simplify:** $135 - 5d + 10d = 215$ 7. **Combine:** $135 + 5d = 215$ 8. **Subtract 135:** $5d = 80$ 9. **Divide:** $d = 16$ 10. **Nickels:** $n = 27 - 16 = 11$ 11. **Answer:** Nickels 11, dimes 16. --- 1. **Problem:** Hamburgers $3, drinks $1, total 145 sold, total 257 funds. 2. **Formula:** Hamburgers $h$, drinks $d$, $h + d = 145$, $3h + d = 257$ 3. **Subtract first from second:** $3h + d - (h + d) = 257 - 145$ 4. **Simplify:** $2h = 112$ 5. **Divide:** $h = 56$ 6. **Drinks:** $d = 145 - 56 = 89$ 7. **Answer:** Hamburgers 56, drinks 89. --- 1. **Problem:** CDs $9, DVDs $11, 20 items sold, total 204. 2. **Formula:** CDs $c$, DVDs $d$, $c + d = 20$, $9c + 11d = 204$ 3. **From first:** $c = 20 - d$ 4. **Substitute:** $9(20 - d) + 11d = 204$ 5. **Simplify:** $180 - 9d + 11d = 204$ 6. **Combine:** $180 + 2d = 204$ 7. **Subtract 180:** $2d = 24$ 8. **Divide:** $d = 12$ 9. **CDs:** $c = 20 - 12 = 8$ 10. **Answer:** CDs 8, DVDs 12. --- 1. **Problem:** Gloves $29, bats $14, 28 items sold, total 647. 2. **Formula:** Gloves $g$, bats $b$, $g + b = 28$, $29g + 14b = 647$ 3. **From first:** $g = 28 - b$ 4. **Substitute:** $29(28 - b) + 14b = 647$ 5. **Simplify:** $812 - 29b + 14b = 647$ 6. **Combine:** $812 - 15b = 647$ 7. **Subtract 812:** $-15b = -165$ 8. **Divide:** $b = 11$ 9. **Gloves:** $g = 28 - 11 = 17$ 10. **Answer:** Gloves 17, bats 11. --- 1. **Problem:** 70 T-shirts, medium $4, large $5, total 320. 2. **Formula:** Medium $m$, large $l$, $m + l = 70$, $4m + 5l = 320$ 3. **From first:** $m = 70 - l$ 4. **Substitute:** $4(70 - l) + 5l = 320$ 5. **Simplify:** $280 - 4l + 5l = 320$ 6. **Combine:** $280 + l = 320$ 7. **Subtract 280:** $l = 40$ 8. **Medium:** $m = 70 - 40 = 30$ 9. **Answer:** Medium 30, large 40. --- 1. **Problem:** Jenny earned 1 less than half Peter's earnings. Together 14. 2. **Formula:** Peter $p$, Jenny $j = \frac{p}{2} - 1$, $p + j = 14$ 3. **Substitute:** $p + \frac{p}{2} - 1 = 14$ 4. **Combine:** $\frac{3p}{2} - 1 = 14$ 5. **Add 1:** $\frac{3p}{2} = 15$ 6. **Multiply both sides by 2:** $3p = 30$ 7. **Divide:** $p = 10$ 8. **Jenny:** $j = \frac{10}{2} - 1 = 5 - 1 = 4$ 9. **Answer:** Peter 10, Jenny 4. --- 1. **Problem:** Bottle and water weigh 9.6 kg. Water weighs 5 times bottle. Find bottle weight. 2. **Formula:** Bottle $b$, water $w = 5b$, total $b + w = 9.6$ 3. **Substitute:** $b + 5b = 9.6$ 4. **Combine:** $6b = 9.6$ 5. **Divide:** $b = 1.6$ 6. **Answer:** Bottle weighs 1.6 kg. --- 1. **Problem:** Blue Jays won 16 more games than lost. Total 162 games. 2. **Formula:** Wins $w$, losses $l$, $w = l + 16$, $w + l = 162$ 3. **Substitute:** $(l + 16) + l = 162$ 4. **Combine:** $2l + 16 = 162$ 5. **Subtract 16:** $2l = 146$ 6. **Divide:** $l = 73$ 7. **Wins:** $w = 73 + 16 = 89$ 8. **Answer:** Wins 89. --- 1. **Problem:** Isosceles triangle, third side 30 m less than twice congruent side. Perimeter 570 m. 2. **Formula:** Congruent side $x$, third side $2x - 30$, perimeter $2x + (2x - 30) = 570$ 3. **Simplify:** $4x - 30 = 570$ 4. **Add 30:** $4x = 600$ 5. **Divide:** $x = 150$ 6. **Third side:** $2(150) - 30 = 300 - 30 = 270$ 7. **Answer:** Congruent sides 150 m, third side 270 m.