The main idea here is to "translate" the words into maths.
First we need to identify the unknowns and label these.
We need to know the number if dimes and the number of quarters. So lets say
x: number of dimes
y: number of quarters
Now lets write equations from the written problem.
We know that there are 36 coind total, thus:
x + y = 36
We also know that the coins total 5.85 dollars, but it is better to count in cents, that is 585 cents.
x are the number of dimes, their value is x*10
y are quarters with value of y*25
thus:
10x+25y=585
We have two equations and two unknowns now, that needs to be solved to get the answer.
x + y = 36
10x+25y=585
Answer: Randomly assign the 1,200 students to <u>6 equal-sized</u> groups. Then select one of the groups and place their names in the bin. Randomly select the winner from the bin.
Step-by-step explanation:
First, let us see how many bins we will need in total.
1,200 students / 200 notecards per bin = 6 bins
Now, the first two options do not give all students a fair chance of winning. They are not our answer.
The last two have a different number of groups. Looking at the calculation we did earlier, we will need 6 equal-sized groups. This means our answer is the last option.
