Question

Emma makes bracelets and necklaces using multi-coloured beads of different sizes. A bracelet consists of a total of beads.A necklace has 56 more beads than a bracelet.a) Write an expression for the total number of beads usedto make a bracelet and a necklace.b) Emma used 100 beads to make a bracelet and a necklace.Find the number of beads used to make the bracelet.

Answer 1

Step-by-step explanation: Once n represents the number of beads used to make a bracelet and n+56 is the number of beads used to make a necklace we have that the total number of beads to make a single bracelet plus a single necklace is given by the following expression

Letter a)

`\begin{gathered} \text{Total}_(beads)=Beads_(bracelet)+Beads_{\text{necklace}} \\ \text{Total}_(beads)=n+(n+56) \\ \text{Total}_(beads)=2n+56 \end{gathered}`

Letter b)

Once Emma has 100 beads we can substitute this value on our expression as follows

`\begin{gathered} \text{Total}_(beads)=2n+56 \\ \text{100}=2n+56 \\ (100-56)/(2)=n \\ n=22 \end{gathered}`

As we can see above the number of beads used to make the bracelet is 22