Respuesta :
Answer:
So the two numbers are {15, 25}.
Step-by-step explanation:
Simultaneous Equations:
xy = 375
x = y + 10
Subsitute the Second One into the First:
(y + 10)y = 375
y^2 + 10y - 375 = 0
y = 15 [and not -25 (natural numbers are not negative)]
Solve for x by Substituing y in the Second Equation:
x = 15 + 10
x = 25
Solution:
So the two numbers are {15, 25}.
Answer:
15 and 25
Step-by-step explanation:
The given relations between the two numbers allow you to write a system of equations. Algebraic solution of the system involves the solution of a quadratic equation. The numbers are "natural numbers", so are both positive integers.
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setup
Let x and y represent the smaller and larger of the two numbers, respectively. The given relations are ...
y = x +10 . . . . . . the larger is 10 more than the smaller
xy = 375 . . . . . . their product is 375
solution
Substituting for y in the second equation, we have ...
x(x +10) = 375
Adding (10/2)² will complete the square.
x² +10x +25 = 375 +25 . . . . add 25
(x +5)² = 400 . . . . . . . . . . . write as a square
x +5 = √400 = 20 . . . . . . positive square root
x = 20 -5 = 15
y = x +10 = 25
Those two numbers are 15 and 25.
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The attachment shows a graphical solution of the equations.
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Additional comment
Your number sense tells you that both numbers end in 5. Their geometric mean is √375 ≈ 19.4, so the first numbers that deserve consideration are numbers ending in 5 that are either side of this value: 15 and 25.
You can also consider their arithmetic mean. If that is represented by z, then we have (z-5)(z+5)=375 ⇒ z²-25=375 ⇒ z²=400 ⇒ z=20, and the two numbers are 20±5.
