Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers

The larger number is 12 and the smaller number is 9

Step-by-step explanation:

Let us first deal with the first sentence of this word problem.

Let's call the larger number  L

and the smaller number  S .

We know from the first sentence:

3 L  = 4 S

We know from the second sentence:

L+S  = 21

Let's solve this second equation for  

L- L+S  = 21 - L

S  = 21 - L

Now we can substitute  21 - L for S  in the first equation and solve for  L :

3L = 4 (21 - L)

3L + 4L = 84 - 4L + 4L

7L = 84

7L/7 = 84/7

L = 12

Next we can substitute 12 for L in the solution to the second equation:

s = 21 - 12

s = 9

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!