第9章数学モデルと幾何

Four-fifths of the people on a hike are children. If there are $12$ children, what is the total number of people on the hike?

The sum of $13$ and twice a number is $-19.$ Find the number.

One number is $3$ less than another number. Their sum is $65.$ Find the numbers.

Bonita has $\text{\$2.95}$ in dimes and quarters in her pocket. If she has $5$ more dimes than quarters, how many of each coin does she have?

At a concert, $\text{\$1600}$ in tickets were sold. Adult tickets were $\text{\$9}$ each and children’s tickets were $\text{\$4}$ each. If the number of adult tickets was $30$ fewer than twice the number of children’s tickets, how many of each kind were sold?

Find the complement of a $\text{52°}$ angle.

The measure of one angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is $14$ more than the measure of the smallest angle. Find the measures of all three angles.

The perimeter of an equilateral triangle is $145$ feet. Find the length of each side.

$\text{Δ}ABC$ is similar to $\text{Δ}XYZ.$ Find the length of side $c.$

Find the length of the missing side. Round to the nearest tenth, if necessary.

Find the length of the missing side. Round to the nearest tenth, if necessary.

A baseball diamond is shaped like a square with sides $90$ feet long. How far is it from home plate to second base, as shown?

The length of a rectangle is $2$ feet more than five times the width. The perimeter is $40$ feet. Find the dimensions of the rectangle.

A triangular poster has base $80$ centimeters and height $55$ centimeters. Find the area of the poster.

A trapezoid has height $14$ inches and bases $20$ inches and $23$ inches. Find the area of the trapezoid.

A circular pool has diameter $90$ inches. What is its circumference? Round to the nearest tenth.

Find the area of the shaded region. Round to the nearest tenth.

Find the volume of a rectangular room with width $12$ feet, length $15$ feet, and height $8$ feet.

A coffee can is shaped like a cylinder with height $7$ inches and radius $5$ inches. Find (a) the surface area and (b) the volume of the can. Round to the nearest tenth.

A traffic cone has height $75$ centimeters. The radius of the base is $20$ centimeters. Find the volume of the cone. Round to the nearest tenth.

Leon drove from his house in Cincinnati to his sister’s house in Cleveland. He drove at a uniform rate of $63$ miles per hour and the trip took $4$ hours. What was the distance?

The Catalina Express takes $1\frac{1}{2}$ hours to travel from Long Beach to Catalina Island, a distance of $22$ miles. To the nearest tenth, what is the speed of the boat?

Solve $x+5y=14$ for $y.$