Subjects algebra

Sum To 119 B99Ed6

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1. **State the problem:** We want to find how to use the numbers 4, 30, 36, 52, and 57 to get the total 119. 2. **Understand the problem:** We need to check if any combination of these numbers adds up to 119. 3. **Try adding all numbers:** $$4 + 30 + 36 + 52 + 57 = 179$$ This is greater than 119, so not all numbers are used. 4. **Try combinations:** - Check if 4 + 30 + 36 + 52 equals 119: $$4 + 30 + 36 + 52 = 122$$ - Check if 30 + 36 + 52 + 57 equals 119: $$30 + 36 + 52 + 57 = 175$$ - Check if 4 + 30 + 57 equals 119: $$4 + 30 + 57 = 91$$ - Check if 4 + 36 + 57 equals 119: $$4 + 36 + 57 = 97$$ - Check if 30 + 36 + 57 equals 119: $$30 + 36 + 57 = 123$$ 5. **Try three numbers combinations:** - 4 + 30 + 52 = 86 - 4 + 36 + 52 = 92 - 30 + 52 + 57 = 139 - 36 + 52 + 57 = 145 6. **Try two numbers combinations:** - 57 + 52 = 109 - 57 + 36 = 93 - 57 + 30 = 87 - 57 + 4 = 61 - 52 + 36 = 88 - 52 + 30 = 82 - 52 + 4 = 56 - 36 + 30 = 66 - 36 + 4 = 40 - 30 + 4 = 34 7. **Try single numbers:** None equal 119. 8. **Try four numbers combinations:** - 4 + 30 + 36 + 57 = 127 - 4 + 30 + 52 + 57 = 143 - 4 + 36 + 52 + 57 = 149 - 30 + 36 + 52 + 57 = 175 9. **Try subtracting numbers from 119:** - 119 - 57 = 62 (not in list) - 119 - 52 = 67 (not in list) - 119 - 36 = 83 (not in list) - 119 - 30 = 89 (not in list) - 119 - 4 = 115 (not in list) 10. **Conclusion:** No simple sum of these numbers equals 119. **Final answer:** It is not possible to get 119 by adding any combination of 4, 30, 36, 52, and 57.