Joshua buys a new TV for $170. He pays for the TV with ten and twenty dollar bills, and uses a total of 11 bills to purchase the TV. How many of each kind of bill did Joshua use to pay for the TV?
Let x be number of 10 dollar bills
And y be number of 20 dollar bills
x + y = 11
10x + 10y = 110
10x + 20y = 170
10 y = 60
y = 6
x = 5
5 , ten dollar bills
6 , 20 dollar bills
If you are supposed to use algebra:
Let x = number of tens,
Let y = number of twenties
x + y = 11 (there are 11 total pieces of paper)
10x + 20y = 170 (10 times the number of tens plus 20 times the number of twenties = the amount of money)
Simplify that by dividing by ten.in
x + 2y = 17
Subtract x + y = 11 from.that
So x = 11 -6 = 5
Check 5(10) +6(20) = 50+120 = 170 checks
If he uses 'x' ten dollar bills and 'y' twenty dollar bills:
x + y = 11 (total of eleven bills)
10x + 20y = 170 (total cost is $170)
Then solve the simultaneous equations:
x = 11 - y
10(11 - y) + 20y = 170
110 - 10y + 20y = 170
10y = 60
y = 6 (six twenty dollar bills)
x = 11 - 6 = 5 (five ten dollar bills)
If they were all 10s, that would take 17
3 20s, that is 3+11
4 20s, that is 4+9
5 20s, that is 5+7
6 20s, that is 6+5 = 11 ⬅
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Answers & Comments
Let x be number of 10 dollar bills
And y be number of 20 dollar bills
x + y = 11
10x + 10y = 110
10x + 20y = 170
10 y = 60
y = 6
x = 5
5 , ten dollar bills
6 , 20 dollar bills
If you are supposed to use algebra:
Let x = number of tens,
Let y = number of twenties
x + y = 11 (there are 11 total pieces of paper)
10x + 20y = 170 (10 times the number of tens plus 20 times the number of twenties = the amount of money)
Simplify that by dividing by ten.in
x + 2y = 17
Subtract x + y = 11 from.that
y = 6
So x = 11 -6 = 5
Check 5(10) +6(20) = 50+120 = 170 checks
If he uses 'x' ten dollar bills and 'y' twenty dollar bills:
x + y = 11 (total of eleven bills)
10x + 20y = 170 (total cost is $170)
Then solve the simultaneous equations:
x = 11 - y
10(11 - y) + 20y = 170
110 - 10y + 20y = 170
10y = 60
y = 6 (six twenty dollar bills)
x = 11 - 6 = 5 (five ten dollar bills)
If they were all 10s, that would take 17
3 20s, that is 3+11
4 20s, that is 4+9
5 20s, that is 5+7
6 20s, that is 6+5 = 11 ⬅