Two groups of students order burritos and tacos at a local restaurant. One order of 3 burritos and 4 tacos costs $11.33. the oth
er order of 9 burritos and 5 tacos costs $23.56.. a. Write a system of equations that describes the situation. b. Solve by elimination to find the cost of a burrito and the cost of a taco.
3 burritos and 4 tacos cost 11.33 3b + 4t = 11.33 <span>9 burritos and 5 tacos cost 23.56 9b + 5t = 23.56 </span> <span>To solve: multiply top equation by 3. </span> <span>3(3b + 4t = 11.33) becomes 9b + 12t = 33.99 </span> <span>9b + 5t = 23.56 stays as is 9b + 5t = 23.56 </span> <span>Now subtract the second equation from the first and you will get </span> <span>7t = 10.43 which you can solve by dividing both sides by 7 to get t = 1.49 so a taco costs $1.49. </span> <span>Now replace a t in either equation with 1.49 so 3b + 4t = 11.33 becomes 3b +4(1.49) = 11.33 or 3b + 5.96 = 11.33. Now subtract 5.96 from each side leaving 3b = 5.37 and finally divide both sides by 3 to get b = 1.79 so a burrito costs $1.79 </span>
<span>Problem Two: </span> <span>3 brass and 10 steel costs $48 3b + 10s = 48 </span> <span>7 brass and 4 steel costs $54 7b + 4s = 54 </span> <span>To solve: multiply top equation by 2 and the bottom equation by 5 so the number of s's will be equal </span> <span>2(3b + 10s = 48) becomes 6b + 20s = 96 </span> <span>5(7b + 4s = 54) becomes 35 b + 20s = 270 </span> <span>Now subtract the top equation from the bottom equation and you will get 29b = 174. Divide both sides by 29 to get b = 6. </span> <span>Now replace the b of either original equations with the 6 (say the top equation) to get 3(6) + 10S = 48 or written another way, </span> <span>10s + 18 = 48. Now subtract 18 from both sides to get 10s = 30 and then divide both sides by 10 to get s = 3. </span> <span>b=6 and s=3 so each brass part is $6 and each steel part is $3.</span>
Y = 3.50x 245 = 3.50x x = 245/3.5 x = 70 coffee mugs
315 = 3.50x x = 315/3.5 x = 90 coffee mugs
Ronny needs to sell 90 coffee mugs to reach his sales goal. However, he already sold 70 coffee mugs, so he needs to sell an additional 20 coffee mugs to reach 90 coffee mugs and reach his $315 sales goal.