Math world problems

Question

Melissa has 15 coins, a mixture of quarters and dimes. How many does she have of each if the value of her coins is $2.40

a) Write the system of linear equations that models the situation.

b) Solve the system using any method. If you use guess and check, show your trails and solution.

Answer 1

D + Q = 15

10D +25Q = 240

multiply 1st equation by 10 and subtract from the 2nd equation

15Q = 90

Q =90/15 = 6 Quarters

D = 15-6 = 9 Dimes

check the solution

10(9) + 25(6) = 90 +150 = 240

9+6 = 15

use substituion or elimination, matrix algebra if you know it, or even trial and error, guess a few times and see if your guess works

Or graph the two equations and find where they intersect

D + Q =15

10D +25Q = 240

2D +5Q = 48

1st requation is a straight line with slope -1 and intercepts (0,15) and (15,0)

2nd or 3rd equation is a straight line with slope = -2.5 and intercepts (0,24) and (9.6,0)

sketch a graph, they intersect at (6,9) with D on the vertical axis, Q on the x axis

with even a rough sketch, you can narrow it down to a few integer possibilities, trial

and error with those 2 or 3 possibilities and Bingo.