Tutor profile: Rashad B.

Two times a number added to three times that same number equals 72. What does this sentence mean mathematically? For bonus points, what is the number?

It's important to translate the English data into algebraic data: "A number" => x "Two times a number" => 2x "Three times that same number" => 3x Thus, the first sentence translates to: 2x + 3x = 72 Bonus: 2x + 3x = 72 ==> adding x 5x = 72 ==> divide by x x = 72/5 = 14.4

Solve using the partial products method. Cayla's school has 258 students. Janet's school has 3 times as many students as Cayla's. How many students are in Janet's school?

Using the given information, the first two sentences can be translated into a product: Janet's school is 3 * the students in Cayla's school, which is 258==> 258 * 3 Now break 258, the larger number, into different numbers representing the place values to create partial products: 258 * 3 = 3 (200 + 50 + 8) = 3 * 200 + 3 *50 + 3 * 8 = 600 + 150 + 24 = 774

Hakeem was selling tickets for the college party he is helping to promote. He sold 40 more online regular tickets than VIP tickets, and he sold twice as many regular tickets at the door than VIP tickets. VIP tickets cost $40, online regular tickets cost $12, and regular tickets at the door cost $20. Hakeem made $3240. How many online regular tickets were sold? How many regular tickets at the door were sold? How many VIP tickets were sold?

It's best to first set up the relevant variables needed to answer the question: Let's set: O= online reg tickets sold D = reg tickets sold at the door V = VIP tickets sold Now, we should create expressions that represent the information given to us in the problem. I "He sold 40 more online regular tickets than VIP tickets" --> O = V + 40 II "He sold twice as many regular tickets at the door than VIP tickets" --> D = 2V This sentence implies a substitution can work: "Hakeem made $3240." Thus the ticket sales (ticket price x # of tickets) added up equal $3240. So: III: V(40) + O(12) +D(20) = 3240 We have existing expressions (I and II) we just developed that we can substitute into equation III 40V + (40+V)(12) + (2V)(20) = 3240 *** ==> multiplication 40V + 480 + 12V + 40V = 3240 ==> adding V 92V + 480 = 3240 ==> subtract 480 92V = 2760 V = 30 *****30 VIP tickets were sold!!**** Using Expression I, O = V + 40 --> O = 30 + V = 70 *******70 online reg tickets were sold!******* Using Expression II, D = 2V ==> D = 60 *****60 tickets at the door were sold!!!!!! ***Verify the solution by resubstituting the sold ticket values: 40(30) + (40+30)(12) + 2*30*20 = 3240