Question

Janet, Li Na, and Katie have 68 beads altogether.Janet has 3 times as many beads as Li Na.Katie has 5 more beads than Janet.How many beads does Katie have?

Answer 1

Step-by-step explanation:

Given;

We are told that Janet, Li Na and Katie all have a total of 68 beads.

We are also told that;

(i) Janet has 3 times as many beads as Li Na

(ii) Katie has 5 more beads than Janet.

Required;

We are required to find out how many beads Katie has.

Step-by-step solution;

From the conditions given, Janet has 3 times as many beads as Li Na. That means if Li has an y number of beads, Janet's would be times 3.

Therefore, if Li Na is L and Janet is J, then it means;

`\begin{gathered} Li\text{ }Na=l \\ Janet=3l \end{gathered}`

Also we are told that Katie has 5 more beads than Janet. That means, if Katie is K, then;

`\begin{gathered} Janet=3l \\ Katie=3l+5 \end{gathered}`

Bear in mind that they all have a total of 68 beads. Hence, we add up their beads as follows;

`\begin{gathered} LiNa+Janet+Katie=68 \\ l+3l+3l+5=68 \end{gathered}`
`7l+5=68`

Subtract 5 from both sides;

`7l+5-5=68-5`
`7l=63`

Divide both sides by 7;

`(7l)/(7)=(63)/(7)`
`l=9`

This means Li Na has 9 beads. If Katie's bead is given by the expression 3l + 5, then she will have;

`\begin{gathered} Katie=3l+5 \\ Katie=3(9)+5 \\ Katie=18+5 \\ Katie=23 \end{gathered}`

ANSWER:

Katie has 23 beads.