Question

Which probem situation can be represented by the equation below?3x +3 <11F Joe and Hannah together got less than 11 questions correct on their quizzes. Joe got 3 more questions correct than Hannah. What is x, the number of quiz questions Hannah got 3 correct?G A coin collection of dimes and quarters has less than 11 coins. The collection has more than 3 times as many quarters as dimes. How many dimes, x, is in the collection?H Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?J The length of a rectangle is 3 inches more than the width, x. Three times the length is less than 11. What is the width of the rectangle?

Answer 1

Let x be correct questions of Joe and y be correct quiz question of Joe. The in equality for Joe and Hannah together questions is,

`x+y<11`

Joe got 3 more questions correct than Hannah, means equaltion is,

`y=x+3`

So inequality obtained is,

`\begin{gathered} x+x+3<11 \\ 2x+3<11 \end{gathered}`

Thus option F is incorrect.

Let x be number of dimes and y be number of quarters. So inequality for collection of coins is,

`x+y<11`

The number of quarters are,

`y=3x`

So resultant inequality is,

`\begin{gathered} x+3x<11 \\ 4x<11 \end{gathered}`

Thus option G is incorrect.

Let larger number be y. So sum of numbers is less than 11, means

`x+y<11`

The equation of larger number in terms of smaller number is,

`y=2x+3`

Substitute the value of y in the inequality to obtain the desired inequality.

`\begin{gathered} x+2x+3<11 \\ 3x+3<11 \end{gathered}`

Thus inequality obtained is 3x + 3 < 11.

Thus option H is correct.

Correct option : Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?