I MetroPCS 912 PM myopenmathcom myopenMath Home MATH 082 F

..: I MetroPCS 9:12 PM myopenmath.com myopenMath Home > MATH 082 Fall 2017>Assessment 4.4 Homework - Value Problems This assignment is past the original due date of Sun 10/22/2017 11:59 pm. You were granted an extension Due Tue 11/21/2017 11:59 pm Questions Grade: 3/10 Print Version people attend a concert and tickets for adults cost If 102 S3 while tickets for children cost $2 and total receipts for the concert was $257, how many of each went to the concert? adults children License Points possible: 1 Unlimited attempts. Message instructor about this question Submit

Solution

1) Here given, there are 102 people in that consert.

Let, x and y be the number of adults and children.

Then, x + y = 102.................(i)

Also given, tickets for adults cost $3 while tickets for children cost $2 and total receipt for that concert was $257.

Therefore, 3x + 2y = 257........................(ii)

Now, to solve this equations, we first multiply (i) by 2 and then substract from (ii), we get,

(3x + 2y) - (2x + 2y) = 257 - 204

i.e., x = 53

Putting this value in (i) we get, y = 49

Hence the number of adults is 53 and the number of children is 49.

2) Let, $A be invested in the account paying 5% annual interest.

Since, Ngoc invests a total of $31,000 in two accounts.

Therefore, $(31,000 - A) is invested in the account paying 4% annual interest.

Here given, after 1 year, Ngoc will get the total interest of $1,420.

Therefore, [(A*5*1)/100] + [(31000 - A)*4*1/100] = 1420

i.e., [(5*A) + (31000 - A)*4] / 100 = 1420

i.e., [(5*A) + 124000 - (4*A)] = 142000

i.e., A + 124000 = 142000

i.e., A = 142000 - 124000

i.e., A = 18000

This implies Ngoc invests $18,000 in the account paying 5% annual interest and $(31,000 - 18,000) ,i.e., $13,000 in the account paying 4% annual interest.