Solve for P given P = 9x − 5y, where x=7 and y=−2. What shape is each face of a cube? A mother is 10 times as…

Question

Solve for P given P = 9x − 5y, where x=7 and y=−2. What shape is each face of a cube? A mother is 10 times as old as her son. In 6 years, she will be four times as old. Find their present ages. Solve

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Here are the solutions to the questions:

39.

Substitute the given values of $x=7$ and $y=-2$ into the expression $P = 9x - 5y$ .
$P = 9(7) - 5(-2)$
Perform the multiplications.
$P = 63 - (-10)$
Simplify the expression.
$P = 63 + 10$ $P = \boxed{73}$
40.
Each face of a cube is in the shape of a Square.
The correct option is c) Square.

2. (a)
Define variables for their present ages.
Let the son's present age be $S$ years.
Let the mother's present age be $M$ years.
Formulate equations based on the given information.
"A mother is 10 times as old as her son":
$M = 10S \quad (1)$
"In 6 years' time, she will be four times as old as her son":
$M+6 = 4(S+6) \quad (2)$
Substitute equation (1) into equation (2).
$10S + 6 = 4(S+6)$ $10S + 6 = 4S + 24$
Solve for $S$ .
$10S - 4S = 24 - 6$ $6S = 18$ $S = \frac{18}{6}$ $S = 3$
Substitute $S=3$ back into equation (1) to find $M$ .
$M = 10(3)$ $M = 30$
The son's present age is 3 years and the mother's present age is 30 years.

2. (b)
Rewrite the equation.
$\frac{x+2}{3} + 2x = 10$
Find a common denominator for the terms on the left side.
$\frac{x+2}{3} + \frac{2x \cdot 3}{3} = 10$ $\frac{x+2+6x}{3} = 10$
Combine like terms in the numerator.
$\frac{7x+2}{3} = 10$
Multiply both sides by 3.
$7x+2 = 10 \times 3$ $7x+2 = 30$
Subtract 2 from both sides.
$7x = 30 - 2$ $7x = 28$
Divide by 7 to solve for $x$ .
$x = \frac{28}{7}$ $x = \boxed{4}$
3. (a)
Calculate the total value of each type of item sold.
Value of 2 guitars: $2 \times \text{N}35,400 = \text{N}70,800$
Value of 5 tennis rackets: $5 \times \text{N}9,900 = \text{N}49,500$
Value of 14 electric kettles: $14 \times \text{N}2,550 = \text{N}35,700$
Calculate the total value of all sales.
$\text{Total sales} = \text{N}70,800 + \text{N}49,500 + \text{N}35,700$ $\text{Total sales} = \text{N}156,000$
Convert the commission percentage to a decimal.
$8\frac{1}{2}\% = 8.5\% = \frac{8.5}{100}$
Calculate the commission.
$\text{Commission} = \frac{8.5}{100} \times \text{N}156,000$ $\text{Commission} = 8.5 \times 1,560$ $\text{Commission} = \boxed{\text{N}13,260}$
3. (b)
Find a common denominator for the two fractions.
The least common multiple of 2 and 3 is 6.
$\frac{5a+2}{2} - \frac{2(3a+1)}{3}$
Rewrite each fraction with the common denominator.
$\frac{3(5a+2)}{6} - \frac{2 \cdot 2(3a+1)}{6}$ $\frac{3(5a+2)}{6} - \frac{4(3a+1)}{6}$
Combine the fractions.
$\frac{3(5a+2) - 4(3a+1)}{6}$
Expand the terms in the numerator.
$\frac{15a + 6 - (12a + 4)}{6}$ $\frac{15a + 6 - 12a - 4}{6}$
Combine like terms in the numerator.
$\frac{(15a - 12a) + (6 - 4)}{6}$ $\frac{3a + 2}{6}$

Solve for P given P = 9x − 5y, where x=7 and y=-2. What shape is each face of a cube? A mother is 10 times as old as her son. In 6 years, she will be four times as old. Find their present ages. Solve

Answer

Step-by-step solution

Substitute the given values of $x=7$ and $y=-2$ into the expression $P = 9x - 5y$ .

Perform the multiplications.

Simplify the expression.

Define variables for their present ages.

Formulate equations based on the given information.

Substitute equation (1) into equation (2).

Solve for $S$ .

Substitute $S=3$ back into equation (1) to find $M$ .

Rewrite the equation.

Find a common denominator for the terms on the left side.

Combine like terms in the numerator.

Multiply both sides by 3.

Subtract 2 from both sides.

Divide by 7 to solve for $x$ .

Calculate the total value of each type of item sold.

Calculate the total value of all sales.

Convert the commission percentage to a decimal.

Calculate the commission.

Find a common denominator for the two fractions.

Rewrite each fraction with the common denominator.

Combine the fractions.

Expand the terms in the numerator.

Combine like terms in the numerator.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Solve for P given P = 9x − 5y, where x=7 and y=-2. What shape is each face of a cube? A mother is 10 times as old as her son. In 6 years, she will be four times as old. Find their present ages. Solve

Answer

Step-by-step solution

Substitute the given values of x=7x=7x=7 and y=−2y=-2y=−2 into the expression P=9x−5yP = 9x - 5yP=9x−5y.

Perform the multiplications.

Simplify the expression.

Define variables for their present ages.

Formulate equations based on the given information.

Substitute equation (1) into equation (2).

Solve for SSS.

Substitute S=3S=3S=3 back into equation (1) to find MMM.

Rewrite the equation.

Find a common denominator for the terms on the left side.

Combine like terms in the numerator.

Multiply both sides by 3.

Subtract 2 from both sides.

Divide by 7 to solve for xxx.

Calculate the total value of each type of item sold.

Calculate the total value of all sales.

Convert the commission percentage to a decimal.

Calculate the commission.

Find a common denominator for the two fractions.

Rewrite each fraction with the common denominator.

Combine the fractions.

Expand the terms in the numerator.

Combine like terms in the numerator.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Substitute the given values of $x=7$ and $y=-2$ into the expression $P = 9x - 5y$ .

Solve for $S$ .

Substitute $S=3$ back into equation (1) to find $M$ .

Divide by 7 to solve for $x$ .