Dawn has been using two bank accounts to save money for a car. the difference between account 1 and account 2 is $100. if she us
2 answers:
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Answer:
The solution of the system of equations is (11, 12)
Step-by-step explanation:
∵ The price of each student ticket is $x
∵ The price of each adult ticket is $y
∵ They sold 3 student tickets and 3 adult tickets for a total of $69
∴ 3x + 3y = 69 ⇒ (1)
∵ they sold 5 student tickets and 3 adults tickets for a total of $91
∴ 5x + 3y = 91 ⇒ (2)
Let us solve the system of equations using the elimination method
→ Subtract equation (1) from equation (2)
∵ (5x - 3x) + (3y - 3y) = (91 - 69)
∴ 2x + 0 = 22
∴ 2x = 22
→ Divide both sides by 2 to find x
∵
∴ x = 11
→ Substitute the value of x in equation (1) or (2) to find y
∵ 3(11) + 3y = 69
∴ 33 + 3y = 69
→ Subtract 33 from both sides
∵ 33 - 33 + 3y = 69 - 33
∴ 3y = 36
→ Divide both sides by 3
∵
∴ y = 12
∴ The solution of the system of equations is (11, 12)
I find it convenient to look at the differences and the rate at which those differences are made up.
8. Jim is closing the $150 gap at the rate of $7.50 per week. He will catch up in
... 150/(7.5/week) = 20 weeks
9. At noon, the price of Stock A has increased by 0.05×3 = 0.15, so is now $15.90, which is $0.63 more than Stock B at that time. The prices are closing the gap at the rate of $0.05 +0.13 = $0.18 per hour, so will be the same after
... $0.63/($0.18/hour) = 3.5 hours . . . . after noon, at 3:30 pm
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You can also write and solve equations for the prices of the stocks. Or you can use a graphing calculator to tell you the solution. When equations are involved, I like to solve them the simplest possible way: let technology do it.
You are given the value at a time, and the rate of change of that value, so the equations are easily written in point-slope form. You will note that the common price at 3:30 pm (15.5 hours after midnight) is one that is not a whole number of cents. (That's usually OK for when trading stocks.)
