Tide-Pool Species: Field Equations

Write and solve one-step equations from a marine biology field study.

Represent the Field Notes

Choose the equation that represents each situation. Use x for the unknown quantity described.

Amara counts 17 limpets on one rock and x limpets on another. She counts 43 limpets in all. Which equation represents her count?

A. 17x = 43B. x + 17 = 43C. x = 43 + 17D. x + 43 = 17

A survey frame marks a small area for counting organisms. Each of 6 frames contains exactly x barnacles. The total is 78 barnacles. Which equation represents the count?

A. 6x = 78B. x + 78 = 6C. 78x = 6D. x + 6 = 78

Luis spends x minutes counting anemones and 3.5 minutes checking the count. Together, these tasks take 11 minutes. Which equation represents the total time?

A. x + 11 = 3.5B. x + 3.5 = 11C. 3.5x = 11D. x = 11 + 3.5

Students divide a straight survey line into x sections. Each section is 3/4 meter long, and the whole line is 6 meters long. Which equation represents the line's length?

A. x + 3/4 = 6B. x = 6 × 3/4C. (3/4)x = 6D. 6x = 3/4

The table shows counts from two tide pools. In Pool B, students count 4 times as many periwinkles as in Pool A. Let x be the missing count in Pool A.

Periwinkle Counts
Tide pool	Periwinkles
A	?
B	52

Which equation represents the relationship?

A. 4x = 52B. x + 4 = 52C. x = 52 × 4D. 52x = 4

Solve the Field Equations

Solve each equation. Write only the number in each blank. Check your solution in the original equation.

Students count 28 mussels in the first pool and x in the second pool. Their equation is x + 28 = 65.

How many mussels are in the second pool? mussels

Eight survey frames each contain x limpets, for a total of 120 limpets. Solve 8x = 120.

How many limpets are in each frame? limpets

A survey line has an unmeasured section x meters long and a measured section 2.75 meters long. Its total length is 7.5 meters. Solve x + 2.75 = 7.5.

How long is the unmeasured section? meters

A team spends x minutes counting snails and 2/3 minute photographing the survey area. These tasks take 1 1/2 minutes in all. Solve x + 2/3 = 1 1/2.

How long does the team spend counting snails? minute

10.

Students mark 6 equal sections along a 4.5-meter survey line. Let x be the length of one section in meters. Solve 6x = 4.5.

How long is one section? meter

Apply and Check

Use one-step equations to complete the field report. Explain your reasoning in the final problem.

11.

The field report lists 12 species for the entire visit. Nine species were already recorded before the final pool was checked. Let x be the number of additional species first recorded in the final pool.

Complete the equation: x + 9 = . How many additional species were first recorded in the final pool? species

12.

Each close-up photograph covers 0.5 square meter of rock. The photographs do not overlap and together cover 3.5 square meters. Let x be the number of photographs.

Complete the equation: 0.5x = . How many photographs were taken?

13.

Nia solves 0.4x = 2 for the number of equal survey sections along a 2-meter line. She writes x = 0.8. Which check correctly identifies her mistake?

A. Since 2 + 0.8 = 2.8, she should add 0.4 to 2 to get 2.4.B. Since 0.4 + 0.8 = 1.2, she should subtract 0.4 from 2 to get 1.6.C. Since 2 × 0.8 = 1.6, she should divide 0.4 by 2 to get 0.2.D. Since 0.4 × 0.8 = 0.32, she should divide 2 by 0.4 to get 5.

14.

A team records 4 crab sightings in its first survey and x crab sightings in its second survey. The combined total is 4 sightings. Write and solve an addition equation for x. A teammate says an unknown count must be greater than zero. Explain why your solution does or does not support that claim.