substitution

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday they paid 15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel Let the number of cups of coffee be c Let the number of bagels be b. Since cost = Price * Quantity, we're...

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold. Let the number of cd's be c and number of...

Pam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the second job, she works as a tutor and makes$12 per hour. One week she worked 30 hours and made$268 . How many hours did she spend at each job? Let the cashier hours be c. Let the tutor hours be t. We're...

Does (6,5) make the equation y = x true x =6 and y = 5, so we have: 5 = 6 which is false. So no, it does not make the equation True.

The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00. Paul sold 15 ivy plants and 6 ferns for 240. What’s the selling price of each plant. Let the cost of each fern be f Let the cost of each ivy plant be I We're given: 12f + 8i = 260 15i + 6f =...

The first group orders 3 pizzas and 4 drinks for $33.50. The second group orders 5 pizzas and 6 drinks for $54. Find the cost for each pizza and each drink Assumptions: Let the cost of each pizza be p Let the cost of each drink be d Givens: 4d + 3p = 33.50 6d + 5p = 54 We have a...

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there? Assumptions: Let the number of adults be a Let the number of kids be k Given with assumptions: a + k = 508 2a + 1.25k = 885.50 (since...

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have? Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations: a + b = 44 10a + 20b = 730 We rearrange equation...

a submarine is 450 feet below sea level. It descends 300 feet. What is its new position? We start at 450 feet below sea level. We descend another 300 feet, so we're now at: -450 - 300 = -750 Negative depth means below sea level, so the submarine is at 750 feet below sea level

In a bike shop they sell bicycles & tricycles. I counted 80 wheels & 34 seats. How many bicycles & tricycles were in the bike shop? Let b be the number or bicycles and t be the number of tricycles. Since each bicycle has 2 wheels and 1 seat and each tricycle has 3 wheels and 1 seat, we have...

46 people showed up to the party. There were 8 less men than women present. How many men were there? Let the number of men be m. Let the number of women be w. We're given two equations: m = w - 8 (8 less men than women) m + w = 46 (46 showed up to the party) Substitute equation (1) into...

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry. Let m be Martha's age. Let h be Harry's age. We're given two equations: m = h + 18 (older means we add) h + m = 106 Substitute equation (1) into equation (2) for m...

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost was $755.25. How many adults and children used the pool Let the number of children who used the pool be c, and the number of adults who used the pool be a. We're given two equations: a + c = 414...

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.5. How many slices of pizza did they sell Let the number of pizza slices be p and the number of hamburgers...

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 327 people entered the park , and the admission fee collected totaled 978.00 dollars . How many children and how many adults were admitted? Let the number of children's tickets be c. Let the number...

(3,-4) lies on the line with equation 3x-2y=k, find k Plug in our values: 3(3) -2(-4) = k 9 + 8 = k k = 17

Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2 equations. Let g be the number of German states. Let a be the number of Austrian states. We're given two equations: a + g = 25 g = a + 7 To solve this system of equations, we substitute...

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? Let the number of drinks be d. Let the number of salads be s. We're given two equations: 2d +...

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you...

Sam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how many dimes? Let d be the number of dimes. Let q be the number of quarters. We're given two equations: 0.1d + 0.25q = 2.25 d + q = 12 We have a simultaneous system of equations. We can solve...