Question

A shop sells wooden beads and crystal beads for \[\$0.20\] and \[\$0.50\] per bead respectively. If a jewellery artist buys 127 beads in total and pays \[\$41\] for them, how much more did she spend on crystal beads than wooden beads?
$\begin{align}
  & A.\$11\\&B.\$15\\&C.\$23\\&D.\$26\\\end{align}$

Answer 1

Hint: First of all, here we need to calculate the amount of crystal beads and wooden beads available. And then we need to find how much she can spend on crystal beads and wooden beads. After that we need to calculate the amount she spent on crystal beads more than wooden beads.

Complete step by step solution:
So, now from the given data we have the seller details i.e. the price details of wooden beads and crystal beads.
Let C be the number of crystal beads
Let W be the number of wooden beads
So from the given data we have that the jewellery artist 127 beads in total.
So, therefore we have,
W + C = 127
W = 127 – C
And she paid $\[\$0.20\] for each wooden bead and $\$0.50$ for each crystal bead, in total she paid $\$41$ for 127 beads.
So, therefore we have
\[\text{W}\times 0.2+\text{C}\times 0.5=41\]
Substituting the value of W = 127 – C in the above equation we have,
$\begin{align}
  & (\text{W }=\text{ }127\text{ }\text{ C})\times 0.2+\text{C}\times 0.5=41 \\
 & 25.4+0.3\times C=41 \\
 & 0.3C=15.6 \\
 & \text{C = }\dfrac{15.6}{0.3} \\
 & C=52 \\
\end{align}$
So, therefore number of crystal beads are C = 52
And now substituting this value of C in W = 127 – C
We have
W = 127 – 52
W = 75
So, therefore number of wooden beads are W = 75
Now, we need to find the amount that she spent on crystal beads than wooden beads,
i.e. 0.5 \[\times \] C – 0.2 \[\times \] W
= 0.5 \[\times \] 52 – 0.2 \[\times \] 75
= 11
So, now the amount she spends on crystal beads than wooden beads is $\$11$.
So, the answer is option (A)

Note: There are chances that the students may make mistakes while forming equations and calculating equations. And another possible mistake that the students can make is by interchanging the values of the cost of wooden beads and crystal beads. They may write the cost of crystal beads as \[\$0.20\] and the cost of wooden beads as \[\$0.50\]. Hence, care should be taken while calculating.