the sum of two numbers is 7 five times the larger number plus four times the the smaller number is 47.
1 answer:
Let x and y represent the larger and smaller numbers, respectively. The problem conditions give rise to two equations:
x + y = 7
5x +4y = 47
You can use the first equation to write an expression for y, then substitute that into the second equation.
y = 7 - x
5x +4(7 -x) = 47 . . . . substitute for y
x + 28 = 47 . . . . . . .. simplify
x = 19 . . . . . . . . . . . . subtract 28
Using our expression for y, we have
y = 7 -19 = -12
The larger number is 19.
The smaller number is -12.
x + y = 7
5x +4y = 47
You can use the first equation to write an expression for y, then substitute that into the second equation.
y = 7 - x
5x +4(7 -x) = 47 . . . . substitute for y
x + 28 = 47 . . . . . . .. simplify
x = 19 . . . . . . . . . . . . subtract 28
Using our expression for y, we have
y = 7 -19 = -12
The larger number is 19.
The smaller number is -12.
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Answer: Choice D
b greater-than 3 and StartFraction 2 over 15 EndFraction
In other words,
b > 3 & 2/15
or
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Explanation:
Let's convert the mixed number 2 & 3/5 into an improper fraction.
We'll use the rule
a & b/c = (a*c + b)/c
In this case, a = 2, b = 3, c = 5
So,
a & b/c = (a*c + b)/c
2 & 3/5 = (2*5 + 3)/5
2 & 3/5 = (10 + 3)/5
2 & 3/5 = 13/5
The inequality is the same as
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Let's multiply both sides by 15 to clear out the fractions
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Now isolate the variable b
Side note: Another way to go from 47/15 to 3 & 2/15 is to notice how
47/15 = 3 remainder 2
The 3 is the whole part while 2 helps form the fractional part. The denominator stays at 15 the whole time.