Question

PLEASE HELP!!

A student needs 3 pieces of wire for a science project. The second piece must be 3 times as long as the first. The third piece must be twice as long as the second. The student has 350 inches of wire to make the three pieces. Let x be the length of the first wire.
a. Write an inequality that models this situation.
b. What are the possible lengths of the shortest piece of wire?
(this is solving inequalities using multiplication or division)

Answer 1

Part a) The inequality that represent the situation is

`x+(3x)+(6x) \leq 350\ in`

Part b) The possible lengths of the shortest piece of wire are all positive real numbers less than or equal to
`35\ inches`

Explanation:

Let

x------> the length of the first wire

3x---> the length of the second wire

2(3x)=6x -----> the length of the third wire

Part a) WRITE AN *INEQUALITY* THAT MODELS THE SITUATION

we know that

The inequality that represent the situation is

`x+(3x)+(6x) \leq 350`

Part b) WHAT ARE THE POSSIBLE LENGTHS OF THE SHORTEST PIECE OF WIRE?

we know that

The shortest piece of wire is the first wire

so

Solve the inequality

`x+(3x)+(6x) \leq 350`

`10x \leq 350`

Divide by 10 both sides

`x \leq 35\ in`

The possible lengths of the shortest piece of wire are all positive real numbers less than or equal to
`35\ inches`