Question

The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, which system of inequalities could represent the values of a and b?
a + b ≥ 30 b ≥ a + 10
a + b ≥ 30 b ≤ a – 10
a + b ≤ 30 b ≥ a + 10
a + b ≤ 30 b ≤ a – 10

Answer 1

SOLUTION

GIVEN

• The sum of two positive integers, a and b, is at least 30

• The difference of the two integers is at least 10

• b is the greater integer

TO CHOOSE THE CORRECT OPTION

The system of inequalities could represent the values of a and b

• a + b ≥ 30, b ≥ a + 10

• a + b ≥ 30, b ≤ a – 10

• a + b ≤ 30 , b ≥ a + 10

• a + b ≤ 30 , b ≤ a – 10

EVALUATION

Here the given two positive integers, a and b

Where b is the greater integer

Since the sum of two positive integers, a and b, is at least 30

$\therefore \: \: \sf{a + b \geqslant 30} \: \: \: \: .......(1)$

Again it is also stated that the difference of the two integers is at least 10

$\therefore \: \sf{b - a \geqslant 10}$

$\therefore \: \sf{b \geqslant a + 10} \: \: \: .....(2)$

Thus inequality (1) & inequality (2) together gives the system of inequalities could represent the values of a and b

$\sf{a + b \geqslant 30 \: \: \: and \: \: b \geqslant a + 10}$

FINAL ANSWER

The system of inequalities could represent the values of a and b

$\sf{a + b \geqslant 30 \: \: \: , \: \: b \geqslant a + 10}$

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