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question:Luis needed to buy some socks. He bought 4 pairs of red socks and 6 pairs of blue ones. In total, he spent x. If the red socks cost 3 each, He paid 5 for each blue pair. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the total amount Luis spent on socks. Let's break down the information given: Number of pairs of red socks: 4 Number of pairs of blue socks: 6 Cost per pair of red socks: 3 Cost per pair of blue socks: 5 Total amount spent: x We can set up the equation as follows: (Number of pairs of red socks * Cost per pair of red socks) + (Number of pairs of blue socks * Cost per pair of blue socks) = Total amount spent (4 * 3) + (6 * 5) = x Let's simplify and solve for x: 12 + 30 = x 42 = x The value of x is 42. 42 The answer is: 42
question:f Grace's mother is 80 years old and her grandmother is twice her mother's age, with Grace's age being 3/8th the age of her grandmother, what is Grace's age?
answer:Grace's grandmother is twice her mother's age, so 80 x 2 = 160 years old. Grace's age is 3/8th the age of her grandmother, so 160 x 3/8 = 60 years old. 60 The answer is: 60
question:f Ambika has four birthday candles and Aniyah has six times as many candles as Ambika, how many birthday candles will they have in total if they combine their candles and divide them equally between themselves?
answer:Ambika has 4 candles. Aniyah has 6 times as many candles as Ambika, so Aniyah has 6 * 4 = 24 candles. If they combine their candles, they will have 4 + 24 = 28 candles. If they divide the candles equally between themselves, each person will have 28 / 2 = 14 candles. 14 The answer is: 14
question:Solve the following system of equations: begin{align*} 3x-5y&=-1.5, 7x+2y&=4.7. end{align*}Express your answer as an ordered pair (x,y) of decimals.
answer:We can solve this system of equations using the method of elimination. Multiplying the first equation by 2 and the second equation by 5, we get: begin{align*} 6x - 10y &= -3, 35x + 10y &= 23.5. end{align*} Adding the two equations, we eliminate the variable y and get: 41x = 20.5. Dividing both sides by 41, we find that x = 0.5. Substituting this value back into the first equation, we can solve for y: begin{align*} 3(0.5) - 5y &= -1.5, 1.5 - 5y &= -1.5, -5y &= -3, y &= 0.6. end{align*} Therefore, the solution to the system of equations is (x, y) = boxed{(0.5, 0.6)}. The answer is: (0.5,0.6)