The sum of two numbers is 45. The larger number is 3 less than twice the smaller. Find the two numbers?
Let's use simultaneous equations for this question. y will be the larger number and x being the smaller number. The sum is 45 so: x + y = 45 (eq1) The larger number is 3 less than twice the smaller number. Changing this to an equation becomes y = 2x - 3 (eq2) Let's use substitution and substitute eq2 into eq1 x + (2x - 3) = 45 Simplify 3x - 3 = 45 Move the -3 to the right hand side, this will change the sign 3x = 45 + 3 3x = 48 Divide both sides by 3 x = 16 Now that we know the value of the smaller number, we can substitute it into eq2 to find y y = 2x - 3 Becomes y = 2(16) - 3 y = 29 Let's check 29 + 16 = 45
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