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breannaasmith1122
24.07.2019 •
Mathematics
The larger of two numbers is 7 more than twice the smaller. if the smaller is subtracted from the larger, the result is 14. find the numbers.
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Ответ:
Let's call the larger number, a, and the smaller number, b.
Equation 1) You know that the larger number (a) is 7 more than twice the smaller number (b):
That means a = 2b (twice the smaller number) + 7 (seven more).
Equation 2) You know that if the smaller number (b) is subtracted from the larger number (a), the result is 14:
That means a - b = 14.
Now you have two equations a = 2b + 7 and a - b = 14, so you can solve for them using a system of equations.
To solve a system of equations, you can use substitution, elimination, or graphing. I will use substitution:
1) Start by solving one equation for a variable. I'll solve a - b = 14 for a, but you can solve for b or solve the other equation for either a or b:
2) Substitute the value of the variable you found from step 1 into the other equation, and solve for the value of the other variable:
3) From step 2, you know the value of one of the variables, b = 7. Substitute this value into either of your original equations to find the value of the other variable, a. I'll be substituting b = 7 into a - b = 14, but you can substitute it into a = 2b + 7:
The value of a = 21 and the value of b = 7.
That means your two numbers are 21 and 7.
Ответ: