Question

practice
example 1
write an equation for each sentence.

1. two added to three times a number m is the same as 18.
2. the product of five and the sum of a number x and three is twelve.
3. the quotient of 24 and x equals 14 minus 2 times x.
4. nine times a number y subtracted from 85 is seven times the sum of four and y.

example 2

1. walking lily has walked 2 miles. her goal is to walk 6 miles. lily plans to reach her goal by walking 3 miles each hour h for the rest of her walk. write an equation to find the number of hours it will take lily to reach her goal.
2. math paulina has completed 24 of the 42 math problems she was assigned for homework. she plans to finish her homework by completing 9 math problems each hour h. write an equation to find the number of hours it will take paulina to complete her math homework assignment
3. athletics of 107 athletes surveyed about what sport they play, some play basketball. of those that play basketball, 48 play baseball and the remaining 33 do not play baseball. write an equation to find the number of athletes surveyed who do not play basketball.
4. sales cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more than three times the number of trucks sold. there were 216,000 cars sold last year. write an equation that can be used to find the number of trucks, t, sold last year.

example 3
translate each sentence into an equation or formula.

1. twice a increased by the cube of a equals b
2. seven less than the sum of p and t is as much as 6.
3. the sum of x and its square is equal to y times z.
4. four times the sum of f and g is identical to six times g.
5. the area a of a square is the length of a side s squared.
6. the perimeter p of a triangle is equal to the sum of the lengths of sides a, b, and c.

Explanation:

Step1: Translate the first - sentence

"Two added to three times a number \(m\) is the same as 18" can be written as \(3m + 2=18\).

Step2: Translate the second - sentence

"The product of five and the sum of a number \(x\) and three is twelve" means \(5(x + 3)=12\).

Step3: Translate the third - sentence

"The quotient of 24 and \(x\) equals 14 minus 2 times \(x\)" gives \(\frac{24}{x}=14 - 2x\).

Step4: Translate the fourth - sentence

"Nine times a number \(y\) subtracted from 85 is seven times the sum of four and \(y\)" is \(85-9y = 7(4 + y)\).

Step5: Translate the fifth - sentence

Lily has walked 2 miles and plans to walk 3 miles each hour \(h\) to reach a 6 - mile goal. So, \(2+3h = 6\).

Step6: Translate the sixth - sentence

Paulina has completed 24 of 42 math problems and plans to finish by doing 9 problems each hour \(h\). The equation is \(24 + 9h=42\).

Step7: Translate the seventh - sentence

Let \(x\) be the number of athletes who do not play basketball. The number of athletes who play basketball is \(48 + 33=81\). So, \(x+81 = 107\).

Step8: Translate the eighth - sentence

The number of cars sold was 39000 more than three times the number of trucks sold. If the number of trucks sold is \(t\) and the number of cars sold is 216000, then \(3t+39000 = 216000\).

Step9: Translate the ninth - sentence

"Twice \(a\) increased by the cube of \(a\) equals \(b\)" is \(2a+a^{3}=b\).

Step10: Translate the tenth - sentence

"Seven less than the sum of \(p\) and \(t\) is as much as 6" gives \((p + t)-7 = 6\).

Step11: Translate the eleventh - sentence

"The sum of \(x\) and its square is equal to \(y\) times \(z\)" is \(x+x^{2}=yz\).

Step12: Translate the twelfth - sentence

"Four times the sum of \(f\) and \(g\) is identical to six times \(g\)" is \(4(f + g)=6g\).

Step13: Translate the thirteenth - sentence

The area \(A\) of a square with side - length \(s\) is \(A=s^{2}\).

Step14: Translate the fourteenth - sentence

The perimeter \(P\) of a triangle with side - lengths \(a\), \(b\), and \(c\) is \(P=a + b + c\).

Answer:

1. \(3m + 2=18\)
2. \(5(x + 3)=12\)
3. \(\frac{24}{x}=14 - 2x\)
4. \(85-9y = 7(4 + y)\)
5. \(2+3h = 6\)
6. \(24 + 9h=42\)
7. \(x+81 = 107\)
8. \(3t+39000 = 216000\)
9. \(2a+a^{3}=b\)
10. \((p + t)-7 = 6\)
11. \(x+x^{2}=yz\)
12. \(4(f + g)=6g\)
13. \(A=s^{2}\)
14. \(P=a + b + c\)