Question

translating systems word problems independent practice
translate each of the following system word problems and type your two equations into the box below each problem.
john has $50 consisting of $5 bills and $1 bills. there are a total of 22 bills all together.
nextel has an initial fee of $125 and charges $50 a month. at&t has an initial fee of $75 and charges $60 per month. after how many months will the cost be the same?
the ski club has 47 members. there are 25 more downhill skiers than there are cross - country skiers.
juan purchased 5 boxes of pencils and 3 boxes of crayons for $8.52. cheyenne purchased 2 boxes of pencils and 4 boxes of crayons for $5.76.
an exam worth 145 points contains 50 questions. some of the questions are worth two points and some are worth five points.
a jacket cost 4 times as much as a pair of shorts. together they cost $75.
samantha has 30 coins consisting of quarters and dimes, which total $5.70.
the perimeter of a rectangular park is 640 yards. the length of the rectangle is 40 yards less than twice the width.
four oranges and five apples cost $3.56. three oranges and four apples cost $2.76.
353 people attend a local play. members get tickets for $2.75 while non - members have to pay $6.50. the total amount earned for the play came to $1762.
at a carnival, three water slide tickets and three ferris wheel tickets cost $17.70. two water slide tickets and three ferris wheel tickets cost $15.55.
to produce a product, it costs acme corporation $50,000 plus $20 per product. if acme sells each item at $25 each, how many must acme sell to break even?
during the techno - geek store sale, 6 blank video tapes and 12 blank dvds cost $35.10. during the same sale, 8 blank video tapes and 3 blank dvds cost $27.95.
you plan to start taking an exercise class. non - members pay $4 per class, while members pay a $10 fee plus $2 per class. after how many classes will the cost be the same?
suppose you have $140 in a bank account. you start saving $5 per week. your friend has $30 in his bank account and saves $10 per week. after how many weeks will you both have the same amount?
a landscaping company placed two orders with a nursery. the first order was for 13 bushes and 4 trees and totaled $487. the second order was for 6 bushes and 2 trees and totaled $232.
at taco hut, 3 tacos and 3 burritos cost $11.25. 4 tacos and 2 burritos cost $10.00.
the sum of two numbers is 45. one number is four times the other.
the lakers scored a total of 80 points in a basketball game against the bulls. the lakers made a total of 37 two - point and three - point shots.
at a festival, jim earned $7343.75 running his food cart. he sold hot dogs for $2.95 and steak sandwiches for $9.95. he sold a total of 985 items.

Explanation:

Step1: Define variables for $5/$1 bills

Let $x$ = number of $5 bills, $y$ = number of $1 bills.
Equation 1 (total bills): $x + y = 22$
Equation 2 (total value): $5x + y = 50$

Step2: Define variables for phone plans

Let $m$ = number of months, $C$ = total cost.
Nextel: $C = 125 + 50m$
AT&T: $C = 75 + 60m$

Step3: Define variables for ski club

Let $c$ = cross-country skiers, $d$ = downhill skiers.
Equation 1 (total members): $c + d = 47$
Equation 2 (skier difference): $d = c + 25$

Step4: Define variables for art supplies

Let $p$ = cost of pencil box, $c$ = cost of crayon box.
Juan: $5p + 3c = 8.52$
Cheyenne: $2p + 4c = 5.76$

Step5: Define variables for exam questions

Let $t$ = 2-point questions, $f$ = 5-point questions.
Equation 1 (total questions): $t + f = 50$
Equation 2 (total points): $2t + 5f = 145$

Step6: Define variables for clothing costs

Let $j$ = jacket cost, $s$ = shorts cost.
Equation 1 (price relationship): $j = 4s$
Equation 2 (total cost): $j + s = 75$

Step7: Define variables for coins

Let $q$ = number of quarters, $d$ = number of dimes.
Equation 1 (total coins): $q + d = 30$
Equation 2 (total value): $0.25q + 0.10d = 5.70$

Step8: Define variables for park dimensions

Let $w$ = width (yards), $l$ = length (yards).
Equation 1 (length relationship): $l = 2w - 40$
Equation 2 (perimeter): $2l + 2w = 640$

Step9: Define variables for fruit costs

Let $o$ = cost of orange, $a$ = cost of apple.
First purchase: $4o + 5a = 3.56$
Second purchase: $3o + 4a = 2.76$

Step10: Define variables for play attendees

Let $m$ = members, $n$ = non-members.
Equation 1 (total attendees): $m + n = 353$
Equation 2 (total revenue): $2.75m + 6.50n = 1762$

Step11: Define variables for carnival tickets

Let $w$ = water slide ticket cost, $f$ = Ferris wheel ticket cost.
First purchase: $3w + 3f = 17.70$
Second purchase: $2w + 3f = 15.55$

Step12: Define variables for break-even

Let $x$ = number of products, $R$ = revenue, $C$ = cost.
Cost: $C = 50000 + 20x$
Revenue: $R = 25x$
Break-even: $50000 + 20x = 25x$

Step13: Define variables for media costs

Let $v$ = video tape cost, $d$ = DVD cost.
First purchase: $6v + 12d = 35.10$
Second purchase: $8v + 3d = 27.95$

Step14: Define variables for exercise classes

Let $c$ = number of classes, $C$ = total cost.
Non-member: $C = 4c$
Member: $C = 10 + 2c$

Step15: Define variables for savings

Let $w$ = number of weeks, $A$ = account balance.
You: $A = 140 + 5w$
Friend: $A = 30 + 10w$

Step16: Define variables for landscaping orders

Let $b$ = bush cost, $t$ = tree cost.
First order: $13b + 4t = 487$
Second order: $6b + 2t = 232$

Step17: Define variables for food costs

Let $t$ = taco cost, $b$ = burrito cost.
First order: $3t + 3b = 11.25$
Second order: $4t + 2b = 10.00$

Step18: Define variables for number pair

Let $x$ = smaller number, $y$ = larger number.
Equation 1 (sum): $x + y = 45$
Equation 2 (relationship): $y = 4x$

Step19: Define variables for basketball shots

Let $t$ = 2-point shots, $h$ = 3-point shots.
Equation 1 (total shots): $t + h = 37$
Equation 2 (total points): $2t + 3h = 80$

Step20: Define variables for festival sales

Let $h$ = hot dogs sold, $s$ = steak sandwiches sold.
Equation 1 (total items): $h + s = 985$
Equation 2 (total revenue): $2.95h + 9.95s = 7343.75$

Answer:

1. $x + y = 22$; $5x + y = 50$
2. $C = 125 + 50m$; $C = 75 + 60m$
3. $c + d = 47$; $d = c + 25$
4. $5p + 3c = 8.52$; $2p + 4c = 5.76$
5. $t + f = 50$; $2t + 5f = 145$
6. $j = 4s$; $j + s = 75$
7. $q + d = 30$; $0.25q + 0.10d = 5.70$
8. $l = 2w - 40$; $2l + 2w = 640$
9. $4o + 5a = 3.56$; $3o + 4a = 2.76$
10. $m + n = 353$; $2.75m + 6.50n = 1762$
11. $3w + 3f = 17.70$; $2w + 3f = 15.55$
12. $50000 + 20x = 25x$
13. $6v + 12d = 35.10$; $8v + 3d = 27.95$
14. $C = 4c$; $C = 10 + 2c$
15. $140 + 5w = 30 + 10w$
16. $13b + 4t = 487$; $6b + 2t = 232$
17. $3t + 3b = 11.25$; $4t + 2b = 10.00$
18. $x + y = 45$; $y = 4x$
19. $t + h = 37$; $2t + 3h = 80$
20. $h + s = 985$; $2.95h + 9.95s = 7343.75$