A fabric store sells two types of ribbon. One customer buys 3 rolls of the lace ribbon and 2 rolls of the satin ribbon and has a
total of 120 yards of ribbon. Another customer buys 2 rolls of the lace ribbon and 4 rolls of the satin ribbon and has a total of 160 yards of ribbon. How many yards are on one roll of lace ribbon and one roll of satin ribbon?
Let L represent the yards in a roll of lace ribbon and S represent the yards in a roll of satin ribbon. We can formulate two equations: 3L + 2S = 120 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). If we multiply Equation 1 by 2 and subtract Equation 2, we have: 6L + 4S = 240 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). Thus, 4L equals 80 yards, leading to L equating to 20 yards. For Equation 1, substituting gives 3(20 yards) + 2S = 120 yards, leading to 2S equal to 60 yards, so S equals 30 yards. Therefore, a roll of lace ribbon contains 20 yards, while a roll of satin ribbon has 30 yards.
The first fraction comes between 27 and 28, leaning towards 28. The second fraction lies between 3 and 4, leaning towards 4. Compatible numbers in division consist of figures that are simple to calculate mentally. 28 divided by 4 results in 7. The estimated quotient will be approximately 7.
At a wage of 8.75 per hour, total earnings for 40 hours would be 350. Calculate overtime at 8.75 times 1.5 which equals 13.13. Then, multiply 13.13 by 12 to get $158. So the total is 350 + 158 = 508, likely around 480 after taxes for the US.
