Question 1154912
let x = the number of 1 dollar bills and y = the number of 5 dollar bills and z = the number of 10 dollar bills.
you get:
x + y + z = 35
x + 5y + 10z = 144
since you have 2 more 10 dollar bills than 5 dollar bills, you get:
z = y + 2
replace z with y + 2 in the first 2 equations to get:
x + y + y + 2 = 35
x + 5y + 10 * (y + 2) = 144
simplify both equations to get:
x + 2y + 2 = 33
x + 5y + 10y + 20 = 144
subtract the constants on the left side of the equation from both sides of the equation and simplify further to get:
x + 2y = 33
x + 15y = 124
subtract the first equation from the first to get:
13y = 91
solve for y to get:
y = 91 / 13 = 7
since z = y + 2, then z = 9
first original equation becomes:
x + 7 + 9 = 35
solve for x to get x = 35 - 16 = 19
you have:
x = 19
y = 7
z = 9
second original equation becomes:
19 * 1 + 7 * 5 + 9 * 10 = 19 + 35 + 90 = 144
both original equations are true when x = 19 and y = 7 and z = 9
you have 19 one dollar bills and 7 five dollar bills and 9 ten dollar bills.
that's your solution.