Answer:
8. Amount invested in savings account A = $950.
Amount invested in savings account B = $550.
9. Students must sell 16 scarves to break-even.
Step-by-step explanation:
8. Let A be the amount invested in savings account A and B be the amount invested in savings account B.
We have been given that amount invested in two savings account is $1500. We can represent this information as:
[tex]A+B=1500...(1)[/tex]
We are also told that after 1 year, we have earned a total of $69.50 in interest. We can represent this information as:
[tex]0.05A+0.04B=69.50...(2)[/tex]
We will use substitution method to solve our system of equations. From equation (1) we will get,
[tex]A=1500-B[/tex]
Upon substituting this value in equation (2) we will get,
[tex]0.05(1500-B)+0.04B=69.50[/tex]
[tex]75-0.05B+0.04B=69.50[/tex]
[tex]75-0.01B=69.50[/tex]
[tex]75-75-0.01B=69.50-75[/tex]
[tex]-0.01B=-5.50[/tex]
[tex]\frac{-0.01B}{-0.01}=\frac{-5.50}{-0.01}[/tex]
[tex]B=550[/tex]
Therefore, the amount invested in savings account B is $550.
Upon substituting B=550 in equation (1) we will get,
[tex]A+550=1500[/tex]
[tex]A+550-550=1500-550[/tex]
[tex]A=950[/tex]
Therefore, the amount invested in savings account A is $950.
9. Let x be the number of scarfs.
We are told that the yarn to make a scarf costs $4. So the cost of yarn for making x scarves will be 4x.
The booth at craft show cost $160 and the cost of a pair new knitting needles is $16. So the total cost of making x scarves will be:
[tex]\text{Total cost of making x scarves}=4x+160+16[/tex]
Since we are told that each scarf sells for $15. So the revenue earned from selling x scarves will be:
[tex]\text{Total revenue earned from selling x scarves}=15x[/tex]
Since we know that break-even point is the point, where total costs are equal to total revenue and total profit at break-even equals 0.
To find the break-even point we will equate total costs to total revenues as:
[tex]4x+160+16=15x[/tex]
Let us solve for x.
[tex]4x+176=15x[/tex]
[tex]4x-4x+176=15x-4x[/tex]
[tex]176=11x[/tex]
[tex]\frac{176}{11}=\frac{11x}{11}[/tex]
[tex]16=x[/tex]
Therefore, the student need to sell 16 scarves to break-even.
