Question

1. in february, pauls electric bill was three dollars more than one - half his gas bill. if the electric bill was ninety - two dollars, what was the gas bill?

answer:

1. zoe bought 16 ounces of frozen yogurt and 7 ounces of toppings from a serve your own frozen yogurt shop for a total of $11.73. if the price of the toppings is $3.57, what is the price of 1 ounce of frozen yogurt?

answer:

1. the first number is eight more than the second number. three times the second number plus twice the first number is equal to 26. find the numbers.

first number:
second number:

1. in march, pauls electric bill was five dollars more than one - third of his gas bill. if the electric bill was $88, what was the gas bill?

answer:

1. 320 tickets were sold to the school play. there were three times as many student tickets sold as adult tickets. find the number of each.

number of adults:
number of students:

1. dan has five times as many $1 bills as $5 bills. he has a total of 48 bills. how many of each does he have?

number of $1 bills:
number of $5 bills:

Explanation:

Step1: Set up equations for problem 8

Let gas - bill be $x$. Electric bill is $92$, and $92=\frac{1}{2}x + 3$.

Step2: Solve for $x$

$92-3=\frac{1}{2}x$, so $89=\frac{1}{2}x$, then $x = 178$.

Step3: Set up equations for problem 9

Let gas - bill be $y$. Electric bill is $88$, and $88=\frac{1}{3}y+5$.

Step4: Solve for $y$

$88 - 5=\frac{1}{3}y$, so $83=\frac{1}{3}y$, then $y = 249$.

Step5: Set up equations for problem 10

Let price per ounce of yogurt be $z$. Total cost is $11.73$ and topping cost is $3.57$. So $16z+3.57 = 11.73$.

Step6: Solve for $z$

$16z=11.73 - 3.57=8.16$, then $z=\frac{8.16}{16}=0.51$.

Step7: Set up equations for problem 11

Let number of adult tickets be $a$ and number of student tickets be $s$. $s = 3a$ and $a + s=320$. Substitute $s$: $a+3a=320$, $4a = 320$, $a = 80$, $s=240$.

Step8: Set up equations for problem 12

Let second number be $m$ and first number be $n$. $n=m + 8$ and $3m+2n=26$. Substitute $n$: $3m+2(m + 8)=26$, $3m+2m+16=26$, $5m=10$, $m = 2$, $n=10$.

Step9: Set up equations for problem 13

Let number of $\$5$ bills be $b$ and number of $\$1$ bills be $c$. $c = 5b$ and $c + b=48$. Substitute $c$: $5b + b=48$, $6b=48$, $b = 8$, $c = 40$.

Answer:

1. $178$
2. $249$
3. $0.51$
4. Number of Adults: $80$, Number of Students: $240$
5. First number: $10$, Second number: $2$
6. Number of $\$1$ bills: $40$, Number of $\$5$ bills: $8$