Question

Rachel can make 3 bracelets in an hour. Oliver can make only 2 bracelets in an hour, but he already has completed 5 bracelets. Explain how she can use a system of equations to determine when she will have the same number of bracelets as oliver.

Answer 1

Hence, she will have the same number of bracelets as oliver after 5 hours.

Explanation:

Rachel can make 3 bracelets in an hour. Oliver can make only 2 bracelets in an hour, but he already has completed 5 bracelets.

Let b be the total number of bracelets made.

so the number of bracelets made by Rachel in 'h' hours is: b=3h

and the number of bracelets made by Oliver in 'h' hours is: b=2h+5.

We are asked to find the value of 'h' so that the number of bracelets made by both of them are equal.

i.e.

3h=2h+5

⇒ 3h-2h=5

⇒ h=5.

Hence, she will have the same number of bracelets as oliver after 5 hours.

( and they will make b=3×5=15 bracelets )

Answer 2

Rachel: 3 bracelets in an hour.
Oliver: 2 bracelets in an hour but has completed 5 bracelets

Rachel : y = 3x
Oliver : y = 2x + 5

Let x be the number of hours. y is the total number of bracelets made in x hours.

3x = 2x + 5
3x - 2x = 5
x = 5

It would take 5 hours for Rachel to have the same number of bracelet as Oliver.

Rachel: 3x = 3(5) = 15
Oliver: 2x + 5 = 2(5) + 5 = 10 + 5 = 15