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One integer is two more than another. The sum of the lesser integer and double the greater is 7. What is the greater integer?
Let x = the greater integer and y = the lesser integer. From the ?rst sentence within the question we get the equation x = y + 2. From the second sentence in the question we get y + 2x = 7. Substitute x = y + 2 within the second equation: y + 2(y + 2) = 7; use the distributive property to simplify to: y + 2y + 4 = 7. Combine like terms to obtain: 3y + 4 = 7; subtract 4 from both sides of the equation: 3y + 4 - 4 = 7 - 4. Simplify to 3y = 3.Divide both sides of the equation through 3: 3y/3 =3/3; thus y = 1. Since the greater is two more than the lesser, the greater is 1 + 2 = 3.
( a+2b)x + (2a - b)y = 2, (a - 2b)x + (2a +b)y = 3 (Ans: 5b - 2a/10ab , a + 10b/10ab ) Ans: 2ax + 4ay = y , we get 4bx - 2by = -1 2ax+ 4ay = 5 4bx- 2by = - 1
a cheeseburger cost $6.39 more than a burger of $2.29, what is the difference?
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1. Show that there do not exist integers x and y for which 110x + 315y = 12. 2. If a and b are odd integers, prove that a 2 +b 2 is divisible by 2 but is NOT divisible by 4. H
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